Results of Confluent Hypergeometric Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 13.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\deriv[2]{w}{z}+(b-z)\deriv{w}{z}-aw = 0} | z*diff(w, [z$(2)])+(b - z)* diff(w, z)- a*w = 0 |
z*D[w, {z, 2}]+(b - z)* D[w, z]- a*w = 0 |
Failure | Failure | Fail -0.-3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-3.999999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-0.+3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}3.999999998-0.*I <- {a = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[0.0, -4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}-4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.0, 4.0] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}4.0 <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}}{\Pochhammersym{b}{s}s!}z^{s}} | KummerM(a, b, z)= sum((pochhammer(a, s))/(pochhammer(b, s)*factorial(s))*(z)^(s), s = 0..infinity) |
Hypergeometric1F1[a, b, z]= Sum[Divide[Pochhammer[a, s],Pochhammer[b, s]*(s)!]*(z)^(s), {s, 0, Infinity}] |
Successful | Successful | - | - |
| 13.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}}{\EulerGamma@{b+s}s!}z^{s}} | KummerM(a, b, z)/GAMMA(b)= sum((pochhammer(a, s))/(GAMMA(b + s)*factorial(s))*(z)^(s), s = 0..infinity) |
Hypergeometric1F1Regularized[a, b, z]= Sum[Divide[Pochhammer[a, s],Gamma[b + s]*(s)!]*(z)^(s), {s, 0, Infinity}] |
Successful | Successful | - | - |
| 13.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z} = \EulerGamma@{b}\OlverconfhyperM@{a}{b}{z}} | KummerM(a, b, z)= GAMMA(b)*KummerM(a, b, z)/GAMMA(b) |
Hypergeometric1F1[a, b, z]= Gamma[b]*Hypergeometric1F1Regularized[a, b, z] |
Successful | Successful | - | - |
| 13.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{b\to-n}\frac{\KummerconfhyperM@{a}{b}{z}}{\EulerGamma@{b}} = \OlverconfhyperM@{a}{-n}{z}} | limit((KummerM(a, b, z))/(GAMMA(b)), b = - n)= KummerM(a, - n, z)/GAMMA(- n) |
Limit[Divide[Hypergeometric1F1[a, b, z],Gamma[b]], b -> - n]= Hypergeometric1F1Regularized[a, - n, z] |
Successful | Successful | - | - |
| 13.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{-n}{z} = \frac{\Pochhammersym{a}{n+1}}{(n+1)!}z^{n+1}\KummerconfhyperM@{a+n+1}{n+2}{z}} | KummerM(a, - n, z)/GAMMA(- n)=(pochhammer(a, n + 1))/(factorial(n + 1))*(z)^(n + 1)* KummerM(a + n + 1, n + 2, z) |
Hypergeometric1F1Regularized[a, - n, z]=Divide[Pochhammer[a, n + 1],(n + 1)!]*(z)^(n + 1)* Hypergeometric1F1[a + n + 1, n + 2, z] |
Failure | Failure | Fail Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Successful |
| 13.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{-m}{b}{z} = (-1)^{m}\Pochhammersym{b}{m}\KummerconfhyperM@{-m}{b}{z}} | KummerU(- m, b, z)=(- 1)^(m)* pochhammer(b, m)*KummerM(- m, b, z) |
HypergeometricU[- m, b, z]=(- 1)^(m)* Pochhammer[b, m]*Hypergeometric1F1[- m, b, z] |
Failure | Failure | Skip | Successful |
| 13.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{m}\Pochhammersym{b}{m}\KummerconfhyperM@{-m}{b}{z} = (-1)^{m}\sum_{s=0}^{m}\binom{m}{s}\Pochhammersym{b+s}{m-s}(-z)^{s}} | (- 1)^(m)* pochhammer(b, m)*KummerM(- m, b, z)=(- 1)^(m)* sum(binomial(m,s)*pochhammer(b + s, m - s)*(- z)^(s), s = 0..m) |
(- 1)^(m)* Pochhammer[b, m]*Hypergeometric1F1[- m, b, z]=(- 1)^(m)* Sum[Binomial[m,s]*Pochhammer[b + s, m - s]*(- z)^(s), {s, 0, m}] |
Successful | Successful | - | - |
| 13.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{a+n+1}{z} = \frac{(-1)^{n}\Pochhammersym{1-a-n}{n}}{z^{a+n}}\KummerconfhyperM@{-n}{1-a-n}{z}} | KummerU(a, a + n + 1, z)=((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))*KummerM(- n, 1 - a - n, z) |
HypergeometricU[a, a + n + 1, z]=Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]*Hypergeometric1F1[- n, 1 - a - n, z] |
Failure | Failure | Skip | Successful |
| 13.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(-1)^{n}\Pochhammersym{1-a-n}{n}}{z^{a+n}}\KummerconfhyperM@{-n}{1-a-n}{z} = z^{-a}\sum_{s=0}^{n}\binom{n}{s}\Pochhammersym{a}{s}z^{-s}} | ((- 1)^(n)* pochhammer(1 - a - n, n))/((z)^(a + n))*KummerM(- n, 1 - a - n, z)= (z)^(- a)* sum(binomial(n,s)*pochhammer(a, s)*(z)^(- s), s = 0..n) |
Divide[(- 1)^(n)* Pochhammer[1 - a - n, n],(z)^(a + n)]*Hypergeometric1F1[- n, 1 - a - n, z]= (z)^(- a)* Sum[Binomial[n,s]*Pochhammer[a, s]*(z)^(- s), {s, 0, n}] |
Failure | Failure | Skip | Successful |
| 13.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{n+1}{z} = \frac{(-1)^{n+1}}{n!\EulerGamma@{a-n}}\sum_{k=0}^{\infty}\frac{\Pochhammersym{a}{k}}{\Pochhammersym{n+1}{k}k!}z^{k}\left(\ln@@{z}+\digamma@{a+k}-\digamma@{1+k}-\digamma@{n+k+1}\right)+\frac{1}{\EulerGamma@{a}}\sum_{k=1}^{n}\frac{(k-1)!\Pochhammersym{1-a+k}{n-k}}{(n-k)!}z^{-k}} | KummerU(a, n + 1, z)=((- 1)^(n + 1))/(factorial(n)*GAMMA(a - n))*sum((pochhammer(a, k))/(pochhammer(n + 1, k)*factorial(k))*(z)^(k)*(ln(z)+ Psi(a + k)- Psi(1 + k)- Psi(n + k + 1)), k = 0..infinity)+(1)/(GAMMA(a))*sum((factorial(k - 1)*pochhammer(1 - a + k, n - k))/(factorial(n - k))*(z)^(- k), k = 1..n) |
HypergeometricU[a, n + 1, z]=Divide[(- 1)^(n + 1),(n)!*Gamma[a - n]]*Sum[Divide[Pochhammer[a, k],Pochhammer[n + 1, k]*(k)!]*(z)^(k)*(Log[z]+ PolyGamma[a + k]- PolyGamma[1 + k]- PolyGamma[n + k + 1]), {k, 0, Infinity}]+Divide[1,Gamma[a]]*Sum[Divide[(k - 1)!*Pochhammer[1 - a + k, n - k],(n - k)!]*(z)^(- k), {k, 1, n}] |
Error | Failure | - | Error |
| 13.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{-m}{n+1}{z} = (-1)^{m}\Pochhammersym{n+1}{m}\KummerconfhyperM@{-m}{n+1}{z}} | KummerU(- m, n + 1, z)=(- 1)^(m)* pochhammer(n + 1, m)*KummerM(- m, n + 1, z) |
HypergeometricU[- m, n + 1, z]=(- 1)^(m)* Pochhammer[n + 1, m]*Hypergeometric1F1[- m, n + 1, z] |
Failure | Failure | Successful | Successful |
| 13.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{m}\Pochhammersym{n+1}{m}\KummerconfhyperM@{-m}{n+1}{z} = (-1)^{m}\sum_{s=0}^{m}\binom{m}{s}\Pochhammersym{n+s+1}{m-s}(-z)^{s}} | (- 1)^(m)* pochhammer(n + 1, m)*KummerM(- m, n + 1, z)=(- 1)^(m)* sum(binomial(m,s)*pochhammer(n + s + 1, m - s)*(- z)^(s), s = 0..m) |
(- 1)^(m)* Pochhammer[n + 1, m]*Hypergeometric1F1[- m, n + 1, z]=(- 1)^(m)* Sum[Binomial[m,s]*Pochhammer[n + s + 1, m - s]*(- z)^(s), {s, 0, m}] |
Successful | Successful | - | - |
| 13.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{-n}{z} = z^{n+1}\KummerconfhyperU@{a+n+1}{n+2}{z}} | KummerU(a, - n, z)= (z)^(n + 1)* KummerU(a + n + 1, n + 2, z) |
HypergeometricU[a, - n, z]= (z)^(n + 1)* HypergeometricU[a + n + 1, n + 2, z] |
Successful | Successful | - | - |
| 13.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{ze^{2\pi\iunit m}} = \frac{2\pi\iunit e^{-\pi\iunit bm}\sin@{\pi bm}}{\EulerGamma@{1+a-b}\sin@{\pi b}}\OlverconfhyperM@{a}{b}{z}+e^{-2\pi\iunit bm}\KummerconfhyperU@{a}{b}{z}} | KummerU(a, b, z*exp(2*Pi*I*m))=(2*Pi*I*exp(- Pi*I*b*m)*sin(Pi*b*m))/(GAMMA(1 + a - b)*sin(Pi*b))*KummerM(a, b, z)/GAMMA(b)+ exp(- 2*Pi*I*b*m)*KummerU(a, b, z) |
HypergeometricU[a, b, z*Exp[2*Pi*I*m]]=Divide[2*Pi*I*Exp[- Pi*I*b*m]*Sin[Pi*b*m],Gamma[1 + a - b]*Sin[Pi*b]]*Hypergeometric1F1Regularized[a, b, z]+ Exp[- 2*Pi*I*b*m]*HypergeometricU[a, b, z] |
Failure | Failure | Fail 584.8702437+1098.665595*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}448650.07-8984458.84*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-.361175805e11+.540703722e11*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}1655.171849-5530.515123*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Skip |
| 13.2.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\OlverconfhyperM@{a}{b}{z},z^{1-b}\OlverconfhyperM@{a-b+1}{2-b}{z}} = \sin@{\pi b}z^{-b}e^{z}/\pi} | (KummerM(a, b, z)/GAMMA(b))*diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))= sin(Pi*b)*(z)^(- b)* exp(z)/ Pi |
Wronskian[{Hypergeometric1F1Regularized[a, b, z], (z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z]}, z]= Sin[Pi*b]*(z)^(- b)* Exp[z]/ Pi |
Failure | Failure | Successful | Skip |
| 13.2.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\OlverconfhyperM@{a}{b}{z},\KummerconfhyperU@{a}{b}{z}} = -\ifrac{z^{-b}e^{z}}{\EulerGamma@{a}}} | (KummerM(a, b, z)/GAMMA(b))*diff(KummerU(a, b, z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(KummerU(a, b, z))= -((z)^(- b)* exp(z))/(GAMMA(a)) |
Wronskian[{Hypergeometric1F1Regularized[a, b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a]] |
Failure | Failure | Successful | Skip |
| 13.2.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\OlverconfhyperM@{a}{b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{+\pi\iunit}z}} = \ifrac{e^{- b\pi\iunit}z^{-b}e^{z}}{\EulerGamma@{b-a}}} | (KummerM(a, b, z)/GAMMA(b))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))=(exp(- b*Pi*I)*(z)^(- b)* exp(z))/(GAMMA(b - a)) |
Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]=Divide[Exp[- b*Pi*I]*(z)^(- b)* Exp[z],Gamma[b - a]] |
Failure | Failure | Skip | Skip |
| 13.2.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\OlverconfhyperM@{a}{b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{-\pi\iunit}z}} = \ifrac{e^{+ b\pi\iunit}z^{-b}e^{z}}{\EulerGamma@{b-a}}} | (KummerM(a, b, z)/GAMMA(b))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff(KummerM(a, b, z)/GAMMA(b), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))=(exp(+ b*Pi*I)*(z)^(- b)* exp(z))/(GAMMA(b - a)) |
Wronskian[{Hypergeometric1F1Regularized[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]=Divide[Exp[+ b*Pi*I]*(z)^(- b)* Exp[z],Gamma[b - a]] |
Failure | Failure | Skip | Skip |
| 13.2.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{z^{1-b}\OlverconfhyperM@{a-b+1}{2-b}{z},\KummerconfhyperU@{a}{b}{z}} = -\ifrac{z^{-b}e^{z}}{\EulerGamma@{a-b+1}}} | ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(KummerU(a, b, z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(KummerU(a, b, z))= -((z)^(- b)* exp(z))/(GAMMA(a - b + 1)) |
Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], HypergeometricU[a, b, z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[a - b + 1]] |
Failure | Failure | Skip | Skip |
| 13.2.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{z^{1-b}\OlverconfhyperM@{a-b+1}{2-b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{+\pi\iunit}z}} = -\ifrac{z^{-b}e^{z}}{\EulerGamma@{1-a}}} | ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a)) |
Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[1 - a]] |
Failure | Failure | Skip | Successful |
| 13.2.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{z^{1-b}\OlverconfhyperM@{a-b+1}{2-b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{-\pi\iunit}z}} = -\ifrac{z^{-b}e^{z}}{\EulerGamma@{1-a}}} | ((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff((z)^(1 - b)* KummerM(a - b + 1, 2 - b, z)/GAMMA(2 - b), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))= -((z)^(- b)* exp(z))/(GAMMA(1 - a)) |
Wronskian[{(z)^(1 - b)* Hypergeometric1F1Regularized[a - b + 1, 2 - b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]= -Divide[(z)^(- b)* Exp[z],Gamma[1 - a]] |
Failure | Failure | Skip | Skip |
| 13.2.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\KummerconfhyperU@{a}{b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{+\pi\iunit}z}} = e^{+(a-b)\pi\iunit}z^{-b}e^{z}} | (KummerU(a, b, z))*diff(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z), z)-diff(KummerU(a, b, z), z)*(exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z))= exp(+(a - b)* Pi*I)*(z)^(- b)* exp(z) |
Wronskian[{HypergeometricU[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z]}, z]= Exp[+(a - b)* Pi*I]*(z)^(- b)* Exp[z] |
Failure | Failure | Skip | Fail
Complex[1040.14465936905, 3523.550863963589] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[13.933478379950422, -18.985981055998398] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[16167.755810004226, 20483.57845334895] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-167.2507901552425, 2.9337620233109254] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.2.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\KummerconfhyperU@{a}{b}{z},e^{z}\KummerconfhyperU@{b-a}{b}{e^{-\pi\iunit}z}} = e^{-(a-b)\pi\iunit}z^{-b}e^{z}} | (KummerU(a, b, z))*diff(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z), z)-diff(KummerU(a, b, z), z)*(exp(z)*KummerU(b - a, b, exp(- Pi*I)*z))= exp(-(a - b)* Pi*I)*(z)^(- b)* exp(z) |
Wronskian[{HypergeometricU[a, b, z], Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z]}, z]= Exp[-(a - b)* Pi*I]*(z)^(- b)* Exp[z] |
Failure | Failure | Skip | Fail
Complex[-26409.287510504182, -21215.250458979182] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[17917.63845480152, -4449.098851771366] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[128856.58558615872, -203204.6357206061] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-130654.53246573739, 11199.95676626326] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.2.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z} = e^{z}\KummerconfhyperM@{b-a}{b}{-z}} | KummerM(a, b, z)= exp(z)*KummerM(b - a, b, - z) |
Hypergeometric1F1[a, b, z]= Exp[z]*Hypergeometric1F1[b - a, b, - z] |
Failure | Successful | Successful | - |
| 13.2.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = z^{1-b}\KummerconfhyperU@{a-b+1}{2-b}{z}} | KummerU(a, b, z)= (z)^(1 - b)* KummerU(a - b + 1, 2 - b, z) |
HypergeometricU[a, b, z]= (z)^(1 - b)* HypergeometricU[a - b + 1, 2 - b, z] |
Successful | Successful | - | - |
| 13.2.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{b}}\KummerconfhyperM@{a}{b}{z} = \frac{e^{- a\pi\iunit}}{\EulerGamma@{b-a}}\KummerconfhyperU@{a}{b}{z}+\frac{e^{+(b-a)\pi\iunit}}{\EulerGamma@{a}}e^{z}\KummerconfhyperU@{b-a}{b}{e^{+\pi\iunit}z}} | (1)/(GAMMA(b))*KummerM(a, b, z)=(exp(- a*Pi*I))/(GAMMA(b - a))*KummerU(a, b, z)+(exp(+(b - a)* Pi*I))/(GAMMA(a))*exp(z)*KummerU(b - a, b, exp(+ Pi*I)*z) |
Divide[1,Gamma[b]]*Hypergeometric1F1[a, b, z]=Divide[Exp[- a*Pi*I],Gamma[b - a]]*HypergeometricU[a, b, z]+Divide[Exp[+(b - a)* Pi*I],Gamma[a]]*Exp[z]*HypergeometricU[b - a, b, Exp[+ Pi*I]*z] |
Failure | Failure | Fail 17637856.16+44349536.15*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}78404.04567+70170.88583*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}23503366.51-739194412.4*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-413147.5251+1810381.777*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 13.2.E41 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{b}}\KummerconfhyperM@{a}{b}{z} = \frac{e^{+ a\pi\iunit}}{\EulerGamma@{b-a}}\KummerconfhyperU@{a}{b}{z}+\frac{e^{-(b-a)\pi\iunit}}{\EulerGamma@{a}}e^{z}\KummerconfhyperU@{b-a}{b}{e^{-\pi\iunit}z}} | (1)/(GAMMA(b))*KummerM(a, b, z)=(exp(+ a*Pi*I))/(GAMMA(b - a))*KummerU(a, b, z)+(exp(-(b - a)* Pi*I))/(GAMMA(a))*exp(z)*KummerU(b - a, b, exp(- Pi*I)*z) |
Divide[1,Gamma[b]]*Hypergeometric1F1[a, b, z]=Divide[Exp[+ a*Pi*I],Gamma[b - a]]*HypergeometricU[a, b, z]+Divide[Exp[-(b - a)* Pi*I],Gamma[a]]*Exp[z]*HypergeometricU[b - a, b, Exp[- Pi*I]*z] |
Failure | Failure | Fail 8.816149469+15.35727015*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}3.036467728-4.734652938*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}237.2244957-69.52948040*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}40.35920508+88.71475163*I <- {a = 2^(1/2)+I*2^(1/2), b = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
Skip |
| 13.2.E42 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{\EulerGamma@{1-b}}{\EulerGamma@{a-b+1}}\KummerconfhyperM@{a}{b}{z}+\frac{\EulerGamma@{b-1}}{\EulerGamma@{a}}z^{1-b}\KummerconfhyperM@{a-b+1}{2-b}{z}} | KummerU(a, b, z)=(GAMMA(1 - b))/(GAMMA(a - b + 1))*KummerM(a, b, z)+(GAMMA(b - 1))/(GAMMA(a))*(z)^(1 - b)* KummerM(a - b + 1, 2 - b, z) |
HypergeometricU[a, b, z]=Divide[Gamma[1 - b],Gamma[a - b + 1]]*Hypergeometric1F1[a, b, z]+Divide[Gamma[b - 1],Gamma[a]]*(z)^(1 - b)* Hypergeometric1F1[a - b + 1, 2 - b, z] |
Successful | Successful | - | - |
| 13.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (b-a)\KummerconfhyperM@{a-1}{b}{z}+(2a-b+z)\KummerconfhyperM@{a}{b}{z}-a\KummerconfhyperM@{a+1}{b}{z} = 0} | (b - a)* KummerM(a - 1, b, z)+(2*a - b + z)* KummerM(a, b, z)- a*KummerM(a + 1, b, z)= 0 |
(b - a)* Hypergeometric1F1[a - 1, b, z]+(2*a - b + z)* Hypergeometric1F1[a, b, z]- a*Hypergeometric1F1[a + 1, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b(b-1)\KummerconfhyperM@{a}{b-1}{z}+b(1-b-z)\KummerconfhyperM@{a}{b}{z}+z(b-a)\KummerconfhyperM@{a}{b+1}{z} = 0} | b*(b - 1)* KummerM(a, b - 1, z)+ b*(1 - b - z)* KummerM(a, b, z)+ z*(b - a)* KummerM(a, b + 1, z)= 0 |
b*(b - 1)* Hypergeometric1F1[a, b - 1, z]+ b*(1 - b - z)* Hypergeometric1F1[a, b, z]+ z*(b - a)* Hypergeometric1F1[a, b + 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a-b+1)\KummerconfhyperM@{a}{b}{z}-a\KummerconfhyperM@{a+1}{b}{z}+(b-1)\KummerconfhyperM@{a}{b-1}{z} = 0} | (a - b + 1)* KummerM(a, b, z)- a*KummerM(a + 1, b, z)+(b - 1)* KummerM(a, b - 1, z)= 0 |
(a - b + 1)* Hypergeometric1F1[a, b, z]- a*Hypergeometric1F1[a + 1, b, z]+(b - 1)* Hypergeometric1F1[a, b - 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b\KummerconfhyperM@{a}{b}{z}-b\KummerconfhyperM@{a-1}{b}{z}-z\KummerconfhyperM@{a}{b+1}{z} = 0} | b*KummerM(a, b, z)- b*KummerM(a - 1, b, z)- z*KummerM(a, b + 1, z)= 0 |
b*Hypergeometric1F1[a, b, z]- b*Hypergeometric1F1[a - 1, b, z]- z*Hypergeometric1F1[a, b + 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b(a+z)\KummerconfhyperM@{a}{b}{z}+z(a-b)\KummerconfhyperM@{a}{b+1}{z}-ab\KummerconfhyperM@{a+1}{b}{z} = 0} | b*(a + z)* KummerM(a, b, z)+ z*(a - b)* KummerM(a, b + 1, z)- a*b*KummerM(a + 1, b, z)= 0 |
b*(a + z)* Hypergeometric1F1[a, b, z]+ z*(a - b)* Hypergeometric1F1[a, b + 1, z]- a*b*Hypergeometric1F1[a + 1, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a-1+z)\KummerconfhyperM@{a}{b}{z}+(b-a)\KummerconfhyperM@{a-1}{b}{z}+(1-b)\KummerconfhyperM@{a}{b-1}{z} = 0} | (a - 1 + z)* KummerM(a, b, z)+(b - a)* KummerM(a - 1, b, z)+(1 - b)* KummerM(a, b - 1, z)= 0 |
(a - 1 + z)* Hypergeometric1F1[a, b, z]+(b - a)* Hypergeometric1F1[a - 1, b, z]+(1 - b)* Hypergeometric1F1[a, b - 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a-1}{b}{z}+(b-2a-z)\KummerconfhyperU@{a}{b}{z}+a(a-b+1)\KummerconfhyperU@{a+1}{b}{z} = 0} | KummerU(a - 1, b, z)+(b - 2*a - z)* KummerU(a, b, z)+ a*(a - b + 1)* KummerU(a + 1, b, z)= 0 |
HypergeometricU[a - 1, b, z]+(b - 2*a - z)* HypergeometricU[a, b, z]+ a*(a - b + 1)* HypergeometricU[a + 1, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (b-a-1)\KummerconfhyperU@{a}{b-1}{z}+(1-b-z)\KummerconfhyperU@{a}{b}{z}+z\KummerconfhyperU@{a}{b+1}{z} = 0} | (b - a - 1)* KummerU(a, b - 1, z)+(1 - b - z)* KummerU(a, b, z)+ z*KummerU(a, b + 1, z)= 0 |
(b - a - 1)* HypergeometricU[a, b - 1, z]+(1 - b - z)* HypergeometricU[a, b, z]+ z*HypergeometricU[a, b + 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z}-a\KummerconfhyperU@{a+1}{b}{z}-\KummerconfhyperU@{a}{b-1}{z} = 0} | KummerU(a, b, z)- a*KummerU(a + 1, b, z)- KummerU(a, b - 1, z)= 0 |
HypergeometricU[a, b, z]- a*HypergeometricU[a + 1, b, z]- HypergeometricU[a, b - 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (b-a)\KummerconfhyperU@{a}{b}{z}+\KummerconfhyperU@{a-1}{b}{z}-z\KummerconfhyperU@{a}{b+1}{z} = 0} | (b - a)* KummerU(a, b, z)+ KummerU(a - 1, b, z)- z*KummerU(a, b + 1, z)= 0 |
(b - a)* HypergeometricU[a, b, z]+ HypergeometricU[a - 1, b, z]- z*HypergeometricU[a, b + 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a+z)\KummerconfhyperU@{a}{b}{z}-z\KummerconfhyperU@{a}{b+1}{z}+a(b-a-1)\KummerconfhyperU@{a+1}{b}{z} = 0} | (a + z)* KummerU(a, b, z)- z*KummerU(a, b + 1, z)+ a*(b - a - 1)* KummerU(a + 1, b, z)= 0 |
(a + z)* HypergeometricU[a, b, z]- z*HypergeometricU[a, b + 1, z]+ a*(b - a - 1)* HypergeometricU[a + 1, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a-1+z)\KummerconfhyperU@{a}{b}{z}-\KummerconfhyperU@{a-1}{b}{z}+(a-b+1)\KummerconfhyperU@{a}{b-1}{z} = 0} | (a - 1 + z)* KummerU(a, b, z)- KummerU(a - 1, b, z)+(a - b + 1)* KummerU(a, b - 1, z)= 0 |
(a - 1 + z)* HypergeometricU[a, b, z]- HypergeometricU[a - 1, b, z]+(a - b + 1)* HypergeometricU[a, b - 1, z]= 0 |
Successful | Successful | - | - |
| 13.3.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a+1)z\KummerconfhyperM@{a+2}{b+2}{z}+(b+1)(b-z)\KummerconfhyperM@{a+1}{b+1}{z}-b(b+1)\KummerconfhyperM@{a}{b}{z} = 0} | (a + 1)* z*KummerM(a + 2, b + 2, z)+(b + 1)*(b - z)* KummerM(a + 1, b + 1, z)- b*(b + 1)* KummerM(a, b, z)= 0 |
(a + 1)* z*Hypergeometric1F1[a + 2, b + 2, z]+(b + 1)*(b - z)* Hypergeometric1F1[a + 1, b + 1, z]- b*(b + 1)* Hypergeometric1F1[a, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a+1)z\KummerconfhyperU@{a+2}{b+2}{z}+(z-b)\KummerconfhyperU@{a+1}{b+1}{z}-\KummerconfhyperU@{a}{b}{z} = 0} | (a + 1)* z*KummerU(a + 2, b + 2, z)+(z - b)* KummerU(a + 1, b + 1, z)- KummerU(a, b, z)= 0 |
(a + 1)* z*HypergeometricU[a + 2, b + 2, z]+(z - b)* HypergeometricU[a + 1, b + 1, z]- HypergeometricU[a, b, z]= 0 |
Successful | Successful | - | - |
| 13.3.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\KummerconfhyperM@{a}{b}{z} = \frac{a}{b}\KummerconfhyperM@{a+1}{b+1}{z}} | diff(KummerM(a, b, z), z)=(a)/(b)*KummerM(a + 1, b + 1, z) |
D[Hypergeometric1F1[a, b, z], z]=Divide[a,b]*Hypergeometric1F1[a + 1, b + 1, z] |
Successful | Successful | - | - |
| 13.3.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\KummerconfhyperM@{a}{b}{z} = \frac{\Pochhammersym{a}{n}}{\Pochhammersym{b}{n}}\KummerconfhyperM@{a+n}{b+n}{z}} | diff(KummerM(a, b, z), [z$(n)])=(pochhammer(a, n))/(pochhammer(b, n))*KummerM(a + n, b + n, z) |
D[Hypergeometric1F1[a, b, z], {z, n}]=Divide[Pochhammer[a, n],Pochhammer[b, n]]*Hypergeometric1F1[a + n, b + n, z] |
Successful | Failure | - | Skip |
| 13.3.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(z^{a-1}\KummerconfhyperM@{a}{b}{z}\right) = \Pochhammersym{a}{n}z^{a+n-1}\KummerconfhyperM@{a+n}{b}{z}} | (z*diff(z, z))^(n)*((z)^(a - 1)* KummerM(a, b, z))= pochhammer(a, n)*(z)^(a + n - 1)* KummerM(a + n, b, z) |
(z*D[z, z])^(n)*((z)^(a - 1)* Hypergeometric1F1[a, b, z])= Pochhammer[a, n]*(z)^(a + n - 1)* Hypergeometric1F1[a + n, b, z] |
Failure | Failure | Fail 2.537884887+11.89104377*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-123.7627467+81.19826795*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-1555.783365-1131.870657*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}-1.589608076+60.84364464*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.3.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{b-1}\KummerconfhyperM@{a}{b}{z}\right) = \Pochhammersym{b-n}{n}z^{b-n-1}\KummerconfhyperM@{a}{b-n}{z}} | diff((z)^(b - 1)* KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)*(z)^(b - n - 1)* KummerM(a, b - n, z) |
D[(z)^(b - 1)* Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n]*(z)^(b - n - 1)* Hypergeometric1F1[a, b - n, z] |
Failure | Failure | Successful | Skip |
| 13.3.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(z^{b-a-1}e^{-z}\KummerconfhyperM@{a}{b}{z}\right) = \Pochhammersym{b-a}{n}z^{b-a+n-1}e^{-z}\KummerconfhyperM@{a-n}{b}{z}} | (z*diff(z, z))^(n)*((z)^(b - a - 1)* exp(- z)*KummerM(a, b, z))= pochhammer(b - a, n)*(z)^(b - a + n - 1)* exp(- z)*KummerM(a - n, b, z) |
(z*D[z, z])^(n)*((z)^(b - a - 1)* Exp[- z]*Hypergeometric1F1[a, b, z])= Pochhammer[b - a, n]*(z)^(b - a + n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b, z] |
Failure | Failure | Fail 1.000000000+0.*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}0.+3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}1.000000000+0.*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.3.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-z}\KummerconfhyperM@{a}{b}{z}\right) = (-1)^{n}\frac{\Pochhammersym{b-a}{n}}{\Pochhammersym{b}{n}}e^{-z}\KummerconfhyperM@{a}{b+n}{z}} | diff(exp(- z)*KummerM(a, b, z), [z$(n)])=(- 1)^(n)*(pochhammer(b - a, n))/(pochhammer(b, n))*exp(- z)*KummerM(a, b + n, z) |
D[Exp[- z]*Hypergeometric1F1[a, b, z], {z, n}]=(- 1)^(n)*Divide[Pochhammer[b - a, n],Pochhammer[b, n]]*Exp[- z]*Hypergeometric1F1[a, b + n, z] |
Failure | Failure | Successful | Skip |
| 13.3.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{b-1}e^{-z}\KummerconfhyperM@{a}{b}{z}\right) = \Pochhammersym{b-n}{n}z^{b-n-1}e^{-z}\KummerconfhyperM@{a-n}{b-n}{z}} | diff((z)^(b - 1)* exp(- z)*KummerM(a, b, z), [z$(n)])= pochhammer(b - n, n)*(z)^(b - n - 1)* exp(- z)*KummerM(a - n, b - n, z) |
D[(z)^(b - 1)* Exp[- z]*Hypergeometric1F1[a, b, z], {z, n}]= Pochhammer[b - n, n]*(z)^(b - n - 1)* Exp[- z]*Hypergeometric1F1[a - n, b - n, z] |
Failure | Failure | Skip | Error |
| 13.3.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\KummerconfhyperU@{a}{b}{z} = -a\KummerconfhyperU@{a+1}{b+1}{z}} | diff(KummerU(a, b, z), z)= - a*KummerU(a + 1, b + 1, z) |
D[HypergeometricU[a, b, z], z]= - a*HypergeometricU[a + 1, b + 1, z] |
Successful | Successful | - | - |
| 13.3.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\KummerconfhyperU@{a}{b}{z} = (-1)^{n}\Pochhammersym{a}{n}\KummerconfhyperU@{a+n}{b+n}{z}} | diff(KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a, n)*KummerU(a + n, b + n, z) |
D[HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a, n]*HypergeometricU[a + n, b + n, z] |
Failure | Successful | Skip | - |
| 13.3.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(z^{a-1}\KummerconfhyperU@{a}{b}{z}\right) = \Pochhammersym{a}{n}\Pochhammersym{a-b+1}{n}z^{a+n-1}\KummerconfhyperU@{a+n}{b}{z}} | (z*diff(z, z))^(n)*((z)^(a - 1)* KummerU(a, b, z))= pochhammer(a, n)*pochhammer(a - b + 1, n)*(z)^(a + n - 1)* KummerU(a + n, b, z) |
(z*D[z, z])^(n)*((z)^(a - 1)* HypergeometricU[a, b, z])= Pochhammer[a, n]*Pochhammer[a - b + 1, n]*(z)^(a + n - 1)* HypergeometricU[a + n, b, z] |
Failure | Failure | Fail .3178044521-.5812355890e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}.5638915996+.3833395878*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}.2833587160+.898459259*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}.2659178351-.5754539144*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.3.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{b-1}\KummerconfhyperU@{a}{b}{z}\right) = (-1)^{n}\Pochhammersym{a-b+1}{n}z^{b-n-1}\KummerconfhyperU@{a}{b-n}{z}} | diff((z)^(b - 1)* KummerU(a, b, z), [z$(n)])=(- 1)^(n)* pochhammer(a - b + 1, n)*(z)^(b - n - 1)* KummerU(a, b - n, z) |
D[(z)^(b - 1)* HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Pochhammer[a - b + 1, n]*(z)^(b - n - 1)* HypergeometricU[a, b - n, z] |
Failure | Failure | Skip | Skip |
| 13.3.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(z^{b-a-1}e^{-z}\KummerconfhyperU@{a}{b}{z}\right) = (-1)^{n}z^{b-a+n-1}e^{-z}\KummerconfhyperU@{a-n}{b}{z}} | (z*diff(z, z))^(n)*((z)^(b - a - 1)* exp(- z)*KummerU(a, b, z))=(- 1)^(n)* (z)^(b - a + n - 1)* exp(- z)*KummerU(a - n, b, z) |
(z*D[z, z])^(n)*((z)^(b - a - 1)* Exp[- z]*HypergeometricU[a, b, z])=(- 1)^(n)* (z)^(b - a + n - 1)* Exp[- z]*HypergeometricU[a - n, b, z] |
Failure | Failure | Fail -.6426838098-.1638932643*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-2.885602225+1.867279788*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-8.024434137+19.17405510*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}.5784828818e-1+.5986041895e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.3.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-z}\KummerconfhyperU@{a}{b}{z}\right) = (-1)^{n}e^{-z}\KummerconfhyperU@{a}{b+n}{z}} | diff(exp(- z)*KummerU(a, b, z), [z$(n)])=(- 1)^(n)* exp(- z)*KummerU(a, b + n, z) |
D[Exp[- z]*HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* Exp[- z]*HypergeometricU[a, b + n, z] |
Failure | Failure | Skip | Skip |
| 13.3.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{b-1}e^{-z}\KummerconfhyperU@{a}{b}{z}\right) = (-1)^{n}z^{b-n-1}e^{-z}\KummerconfhyperU@{a-n}{b-n}{z}} | diff((z)^(b - 1)* exp(- z)*KummerU(a, b, z), [z$(n)])=(- 1)^(n)* (z)^(b - n - 1)* exp(- z)*KummerU(a - n, b - n, z) |
D[(z)^(b - 1)* Exp[- z]*HypergeometricU[a, b, z], {z, n}]=(- 1)^(n)* (z)^(b - n - 1)* Exp[- z]*HypergeometricU[a - n, b - n, z] |
Error | Failure | - | Error |
| 13.3.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n} = z^{n}\deriv[n]{}{z}z^{n}} | (z*diff(z, z))^(n)= (z)^(n)* diff((z)^(n), [z$(n)]) |
(z*D[z, z])^(n)= (z)^(n)* D[(z)^(n), {z, n}] |
Failure | Failure | Fail 28.28427122-28.28427122*I <- {z = 2^(1/2)+I*2^(1/2), n = 3}28.28427122+28.28427122*I <- {z = 2^(1/2)-I*2^(1/2), n = 3}-28.28427122+28.28427122*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}-28.28427122-28.28427122*I <- {z = -2^(1/2)+I*2^(1/2), n = 3} |
Fail
Complex[28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-28.284271247461902, 28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-28.284271247461902, -28.284271247461902] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = \frac{1}{\EulerGamma@{a}\EulerGamma@{b-a}}\int_{0}^{1}e^{zt}t^{a-1}(1-t)^{b-a-1}\diff{t}} | KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(a)*GAMMA(b - a))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = 0..1) |
Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[a]*Gamma[b - a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, 0, 1}] |
Successful | Failure | - | Skip |
| 13.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = \frac{1}{\EulerGamma@{b-c}}\int_{0}^{1}\OlverconfhyperM@{a}{c}{zt}t^{c-1}(1-t)^{b-c-1}\diff{t}} | KummerM(a, b, z)/GAMMA(b)=(1)/(GAMMA(b - c))*int(KummerM(a, c, z*t)/GAMMA(c)*(t)^(c - 1)*(1 - t)^(b - c - 1), t = 0..1) |
Hypergeometric1F1Regularized[a, b, z]=Divide[1,Gamma[b - c]]*Integrate[Hypergeometric1F1Regularized[a, c, z*t]*(t)^(c - 1)*(1 - t)^(b - c - 1), {t, 0, 1}] |
Successful | Failure | - | Skip |
| 13.4.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{-z} = \frac{z^{\frac{1}{2}-\frac{1}{2}b}}{\EulerGamma@{a}}\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}b-\frac{1}{2}}\BesselJ{b-1}@{2\sqrt{zt}}\diff{t}} | KummerM(a, b, - z)/GAMMA(b)=((z)^((1)/(2)-(1)/(2)*b))/(GAMMA(a))*int(exp(- t)*(t)^(a -(1)/(2)*b -(1)/(2))* BesselJ(b - 1, 2*sqrt(z*t)), t = 0..infinity) |
Hypergeometric1F1Regularized[a, b, - z]=Divide[(z)^(Divide[1,2]-Divide[1,2]*b),Gamma[a]]*Integrate[Exp[- t]*(t)^(a -Divide[1,2]*b -Divide[1,2])* BesselJ[b - 1, 2*Sqrt[z*t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{\infty}e^{-zt}t^{a-1}(1+t)^{b-a-1}\diff{t}} | KummerU(a, b, z)=(1)/(GAMMA(a))*int(exp(- z*t)*(t)^(a - 1)*(1 + t)^(b - a - 1), t = 0..infinity) |
HypergeometricU[a, b, z]=Divide[1,Gamma[a]]*Integrate[Exp[- z*t]*(t)^(a - 1)*(1 + t)^(b - a - 1), {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 13.4.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{z^{1-a}}{\EulerGamma@{a}\EulerGamma@{1+a-b}}\int_{0}^{\infty}\frac{\KummerconfhyperU@{b-a}{b}{t}e^{-t}t^{a-1}}{t+z}\diff{t}} | KummerU(a, b, z)=((z)^(1 - a))/(GAMMA(a)*GAMMA(1 + a - b))*int((KummerU(b - a, b, t)*exp(- t)*(t)^(a - 1))/(t + z), t = 0..infinity) |
HypergeometricU[a, b, z]=Divide[(z)^(1 - a),Gamma[a]*Gamma[1 + a - b]]*Integrate[Divide[HypergeometricU[b - a, b, t]*Exp[- t]*(t)^(a - 1),t + z], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{(-1)^{n}z^{1-b-n}}{\EulerGamma@{1+a-b}}\int_{0}^{\infty}\frac{\OlverconfhyperM@{b-a}{b}{t}e^{-t}t^{b+n-1}}{t+z}\diff{t}} | KummerU(a, b, z)=((- 1)^(n)* (z)^(1 - b - n))/(GAMMA(1 + a - b))*int((KummerM(b - a, b, t)/GAMMA(b)*exp(- t)*(t)^(b + n - 1))/(t + z), t = 0..infinity) |
HypergeometricU[a, b, z]=Divide[(- 1)^(n)* (z)^(1 - b - n),Gamma[1 + a - b]]*Integrate[Divide[Hypergeometric1F1Regularized[b - a, b, t]*Exp[- t]*(t)^(b + n - 1),t + z], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{2z^{\frac{1}{2}-\frac{1}{2}b}}{\EulerGamma@{a}\EulerGamma@{a-b+1}}\*\int_{0}^{\infty}e^{-t}t^{a-\frac{1}{2}b-\frac{1}{2}}\modBesselK{b-1}@{2\sqrt{zt}}\diff{t}} | KummerU(a, b, z)=(2*(z)^((1)/(2)-(1)/(2)*b))/(GAMMA(a)*GAMMA(a - b + 1))* int(exp(- t)*(t)^(a -(1)/(2)*b -(1)/(2))* BesselK(b - 1, 2*sqrt(z*t)), t = 0..infinity) |
HypergeometricU[a, b, z]=Divide[2*(z)^(Divide[1,2]-Divide[1,2]*b),Gamma[a]*Gamma[a - b + 1]]* Integrate[Exp[- t]*(t)^(a -Divide[1,2]*b -Divide[1,2])* BesselK[b - 1, 2*Sqrt[z*t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 13.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = z^{c-a}\*\int_{0}^{\infty}e^{-zt}t^{c-1}\genhyperOlverF{2}{1}@{a,a-b+1}{c}{-t}\diff{t}} | KummerU(a, b, z)= (z)^(c - a)* int(exp(- z*t)*(t)^(c - 1)* hypergeom([a , a - b + 1], [c], - t), t = 0..infinity) |
HypergeometricU[a, b, z]= (z)^(c - a)* Integrate[Exp[- z*t]*(t)^(c - 1)* HypergeometricPFQRegularized[{a , a - b + 1}, {c}, - t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = \frac{\EulerGamma@{1+a-b}}{2\pi\iunit\EulerGamma@{a}}\int_{0}^{(1+)}e^{zt}t^{a-1}{(t-1)^{b-a-1}}\diff{t}} | KummerM(a, b, z)/GAMMA(b)=(GAMMA(1 + a - b))/(2*Pi*I*GAMMA(a))*int(exp(z*t)*(t)^(a - 1)*(t - 1)^(b - a - 1), t = 0..(1 +)) |
Hypergeometric1F1Regularized[a, b, z]=Divide[Gamma[1 + a - b],2*Pi*I*Gamma[a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(t - 1)^(b - a - 1), {t, 0, (1 +)}] |
Error | Failure | - | Error |
| 13.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = e^{-a\pi\iunit}\frac{\EulerGamma@{1-a}}{2\pi\iunit\EulerGamma@{b-a}}\int_{1}^{(0+)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\diff{t}} | KummerM(a, b, z)/GAMMA(b)= exp(- a*Pi*I)*(GAMMA(1 - a))/(2*Pi*I*GAMMA(b - a))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = 1..(0 +)) |
Hypergeometric1F1Regularized[a, b, z]= Exp[- a*Pi*I]*Divide[Gamma[1 - a],2*Pi*I*Gamma[b - a]]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, 1, (0 +)}] |
Error | Failure | - | Error |
| 13.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = e^{-b\pi\iunit}\EulerGamma@{1-a}\EulerGamma@{1+a-b}\*\frac{1}{4\pi^{2}}\int_{\alpha}^{(0+,1+,0-,1-)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\diff{t}} | KummerM(a, b, z)/GAMMA(b)= exp(- b*Pi*I)*GAMMA(1 - a)*GAMMA(1 + a - b)*(1)/(4*(Pi)^(2))*int(exp(z*t)*(t)^(a - 1)*(1 - t)^(b - a - 1), t = alpha..(0 + , 1 + , 0 - , 1 -)) |
Hypergeometric1F1Regularized[a, b, z]= Exp[- b*Pi*I]*Gamma[1 - a]*Gamma[1 + a - b]*Divide[1,4*(Pi)^(2)]*Integrate[Exp[z*t]*(t)^(a - 1)*(1 - t)^(b - a - 1), {t, \[Alpha], (0 + , 1 + , 0 - , 1 -)}] |
Error | Failure | - | Error |
| 13.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{c}{z} = \frac{\EulerGamma@{b}}{2\pi\iunit}z^{1-b}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}\genhyperOlverF{2}{1}@{a,b}{c}{\ifrac{1}{t}}\diff{t}} | KummerM(a, c, z)/GAMMA(c)=(GAMMA(b))/(2*Pi*I)*(z)^(1 - b)* int(exp(z*t)*(t)^(- b)* hypergeom([a , b], [c], (1)/(t)), t = - infinity..(0 + , 1 +)) |
Hypergeometric1F1Regularized[a, c, z]=Divide[Gamma[b],2*Pi*I]*(z)^(1 - b)* Integrate[Exp[z*t]*(t)^(- b)* HypergeometricPFQRegularized[{a , b}, {c}, Divide[1,t]], {t, - Infinity, (0 + , 1 +)}] |
Error | Failure | - | Error |
| 13.4.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{z} = \frac{z^{1-b}}{2\pi\iunit}\int_{-\infty}^{(0+,1+)}e^{zt}t^{-b}\!\left(1-\frac{1}{t}\right)^{-a}\diff{t}} | KummerM(a, b, z)/GAMMA(b)=((z)^(1 - b))/(2*Pi*I)*int(exp(z*t)*(t)^(- b)*(1 -(1)/(t))^(- a), t = - infinity..(0 + , 1 +)) |
Hypergeometric1F1Regularized[a, b, z]=Divide[(z)^(1 - b),2*Pi*I]*Integrate[Exp[z*t]*(t)^(- b)*(1 -Divide[1,t])^(- a), {t, - Infinity, (0 + , 1 +)}] |
Error | Failure | - | Error |
| 13.4.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = e^{-a\pi\iunit}\frac{\EulerGamma@{1-a}}{2\pi\iunit}\int_{\infty}^{(0+)}e^{-zt}t^{a-1}{(1+t)^{b-a-1}}\diff{t}} | KummerU(a, b, z)= exp(- a*Pi*I)*(GAMMA(1 - a))/(2*Pi*I)*int(exp(- z*t)*(t)^(a - 1)*(1 + t)^(b - a - 1), t = infinity..(0 +)) |
HypergeometricU[a, b, z]= Exp[- a*Pi*I]*Divide[Gamma[1 - a],2*Pi*I]*Integrate[Exp[- z*t]*(t)^(a - 1)*(1 + t)^(b - a - 1), {t, Infinity, (0 +)}] |
Error | Failure | - | Error |
| 13.4.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\KummerconfhyperU@{a}{b}{z}}{\EulerGamma@{c}\EulerGamma@{c-b+1}} = \frac{z^{1-c}}{2\pi\iunit}\int_{-\infty}^{(0+)}e^{zt}t^{-c}\genhyperOlverF{2}{1}@{a,c}{a+c-b+1}{1-\frac{1}{t}}\diff{t}} | (KummerU(a, b, z))/(GAMMA(c)*GAMMA(c - b + 1))=((z)^(1 - c))/(2*Pi*I)*int(exp(z*t)*(t)^(- c)* hypergeom([a , c], [a + c - b + 1], 1 -(1)/(t)), t = - infinity..(0 +)) |
Divide[HypergeometricU[a, b, z],Gamma[c]*Gamma[c - b + 1]]=Divide[(z)^(1 - c),2*Pi*I]*Integrate[Exp[z*t]*(t)^(- c)* HypergeometricPFQRegularized[{a , c}, {a + c - b + 1}, 1 -Divide[1,t]], {t, - Infinity, (0 +)}] |
Error | Failure | - | Error |
| 13.4.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \OlverconfhyperM@{a}{b}{-z} = \frac{1}{2\pi\iunit\EulerGamma@{a}}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{a+t}\EulerGamma@{-t}}{\EulerGamma@{b+t}}z^{t}\diff{t}} | KummerM(a, b, - z)/GAMMA(b)=(1)/(2*Pi*I*GAMMA(a))*int((GAMMA(a + t)*GAMMA(- t))/(GAMMA(b + t))*(z)^(t), t = - I*infinity..I*infinity) |
Hypergeometric1F1Regularized[a, b, - z]=Divide[1,2*Pi*I*Gamma[a]]*Integrate[Divide[Gamma[a + t]*Gamma[- t],Gamma[b + t]]*(z)^(t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{z^{-a}}{2\pi\iunit}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{a+t}\EulerGamma@{1+a-b+t}\EulerGamma@{-t}}{\EulerGamma@{a}\EulerGamma@{1+a-b}}z^{-t}\diff{t}} | KummerU(a, b, z)=((z)^(- a))/(2*Pi*I)*int((GAMMA(a + t)*GAMMA(1 + a - b + t)*GAMMA(- t))/(GAMMA(a)*GAMMA(1 + a - b))*(z)^(- t), t = - I*infinity..I*infinity) |
HypergeometricU[a, b, z]=Divide[(z)^(- a),2*Pi*I]*Integrate[Divide[Gamma[a + t]*Gamma[1 + a - b + t]*Gamma[- t],Gamma[a]*Gamma[1 + a - b]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 13.4.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = \frac{z^{1-b}e^{z}}{2\pi\iunit}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{b-1+t}\EulerGamma@{t}}{\EulerGamma@{a+t}}z^{-t}\diff{t}} | KummerU(a, b, z)=((z)^(1 - b)* exp(z))/(2*Pi*I)*int((GAMMA(b - 1 + t)*GAMMA(t))/(GAMMA(a + t))*(z)^(- t), t = - I*infinity..I*infinity) |
HypergeometricU[a, b, z]=Divide[(z)^(1 - b)* Exp[z],2*Pi*I]*Integrate[Divide[Gamma[b - 1 + t]*Gamma[t],Gamma[a + t]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 13.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{a}{z} = e^{z}} | KummerM(a, a, z)= exp(z) |
Hypergeometric1F1[a, a, z]= Exp[z] |
Successful | Successful | - | - |
| 13.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{1}{2}{2z} = \frac{e^{z}}{z}\sinh@@{z}} | KummerM(1, 2, 2*z)=(exp(z))/(z)*sinh(z) |
Hypergeometric1F1[1, 2, 2*z]=Divide[Exp[z],z]*Sinh[z] |
Successful | Successful | - | - |
| 13.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{0}{b}{z} = \KummerconfhyperU@{0}{b}{z}} | KummerM(0, b, z)= KummerU(0, b, z) |
Hypergeometric1F1[0, b, z]= HypergeometricU[0, b, z] |
Successful | Successful | - | - |
| 13.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{0}{b}{z} = 1} | KummerU(0, b, z)= 1 |
HypergeometricU[0, b, z]= 1 |
Successful | Successful | - | - |
| 13.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{a+1}{z} = z^{-a}} | KummerU(a, a + 1, z)= (z)^(- a) |
HypergeometricU[a, a + 1, z]= (z)^(- a) |
Failure | Successful | Successful | - |
| 13.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{a+1}{-z} = e^{-z}\KummerconfhyperM@{1}{a+1}{z}} | KummerM(a, a + 1, - z)= exp(- z)*KummerM(1, a + 1, z) |
Hypergeometric1F1[a, a + 1, - z]= Exp[- z]*Hypergeometric1F1[1, a + 1, z] |
Successful | Successful | - | - |
| 13.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-z}\KummerconfhyperM@{1}{a+1}{z} = az^{-a}\incgamma@{a}{z}} | exp(- z)*KummerM(1, a + 1, z)= a*(z)^(- a)* GAMMA(a)-GAMMA(a, z) |
Exp[- z]*Hypergeometric1F1[1, a + 1, z]= a*(z)^(- a)* Gamma[a, 0, z] |
Failure | Successful | Fail -.577162386e-1+.3563618752*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.4492199205+.4890257481*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}21.39901789+84.08885044*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}10.80783636-3.379514632*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 13.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{a}{z} = z^{1-a}\KummerconfhyperU@{1}{2-a}{z}} | KummerU(a, a, z)= (z)^(1 - a)* KummerU(1, 2 - a, z) |
HypergeometricU[a, a, z]= (z)^(1 - a)* HypergeometricU[1, 2 - a, z] |
Successful | Successful | - | - |
| 13.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{1-a}\KummerconfhyperU@{1}{2-a}{z} = z^{1-a}e^{z}\genexpintE{a}@{z}} | (z)^(1 - a)* KummerU(1, 2 - a, z)= (z)^(1 - a)* exp(z)*Ei(a, z) |
(z)^(1 - a)* HypergeometricU[1, 2 - a, z]= (z)^(1 - a)* Exp[z]*ExpIntegralE[a, z] |
Successful | Successful | - | - |
| 13.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{1-a}e^{z}\genexpintE{a}@{z} = e^{z}\incGamma@{1-a}{z}} | (z)^(1 - a)* exp(z)*Ei(a, z)= exp(z)*GAMMA(1 - a, z) |
(z)^(1 - a)* Exp[z]*ExpIntegralE[a, z]= Exp[z]*Gamma[1 - a, z] |
Successful | Successful | - | - |
| 13.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{\sqrt{\pi}}{2z}\erf@{z}} | KummerM((1)/(2), (3)/(2), - (z)^(2))=(sqrt(Pi))/(2*z)*erf(z) |
Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]=Divide[Sqrt[Pi],2*z]*Erf[z] |
Successful | Successful | - | - |
| 13.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \sqrt{\pi}e^{z^{2}}\erfc@{z}} | KummerU((1)/(2), (1)/(2), (z)^(2))=sqrt(Pi)*exp((z)^(2))*erfc(z) |
HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]=Sqrt[Pi]*Exp[(z)^(2)]*Erfc[z] |
Failure | Failure | Fail 3.075886301+2.075744094*I <- {z = -2^(1/2)-I*2^(1/2)}3.075886301-2.075744094*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[3.0758862951142576, 2.0757440991874905] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.0758862951142576, -2.0757440991874905] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{\nu+\tfrac{1}{2}}{2\nu+1}{2z} = \EulerGamma@{1+\nu}e^{z}\left(\ifrac{z}{2}\right)^{-\nu}\modBesselI{\nu}@{z}} | KummerM(nu +(1)/(2), 2*nu + 1, 2*z)= GAMMA(1 + nu)*exp(z)*((z)/(2))^(- nu)* BesselI(nu, z) |
Hypergeometric1F1[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z]= Gamma[1 + \[Nu]]*Exp[z]*(Divide[z,2])^(- \[Nu])* BesselI[\[Nu], z] |
Successful | Successful | - | - |
| 13.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\nu+\tfrac{1}{2}}{2\nu+1}{2z} = \frac{1}{\sqrt{\pi}}e^{z}\left(2z\right)^{-\nu}\modBesselK{\nu}@{z}} | KummerU(nu +(1)/(2), 2*nu + 1, 2*z)=(1)/(sqrt(Pi))*exp(z)*(2*z)^(- nu)* BesselK(nu, z) |
HypergeometricU[\[Nu]+Divide[1,2], 2*\[Nu]+ 1, 2*z]=Divide[1,Sqrt[Pi]]*Exp[z]*(2*z)^(- \[Nu])* BesselK[\[Nu], z] |
Successful | Successful | - | - |
| 13.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\tfrac{5}{6}}{\tfrac{5}{3}}{\tfrac{4}{3}z^{3/2}} = \sqrt{\pi}\frac{3^{5/6}\exp@{\tfrac{2}{3}z^{3/2}}}{2^{2/3}z}\AiryAi@{z}} | KummerU((5)/(6), (5)/(3), (4)/(3)*(z)^(3/ 2))=sqrt(Pi)*((3)^(5/ 6)* exp((2)/(3)*(z)^(3/ 2)))/((2)^(2/ 3)* z)*AiryAi(z) |
HypergeometricU[Divide[5,6], Divide[5,3], Divide[4,3]*(z)^(3/ 2)]=Sqrt[Pi]*Divide[(3)^(5/ 6)* Exp[Divide[2,3]*(z)^(3/ 2)],(2)^(2/ 3)* z]*AiryAi[z] |
Failure | Failure | Fail .1287113381-.3250284300*I <- {z = -2^(1/2)-I*2^(1/2)}.1287113381+.3250284300*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.12871133806471044, -0.32502842978110724] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.12871133806471044, 0.32502842978110724] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a+\frac{1}{4}}e^{\frac{1}{4}z^{2}}\paraU@{a}{z}} | KummerU((1)/(2)*a +(1)/(4), (1)/(2), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a +(1)/(4))* exp((1)/(4)*(z)^(2))*CylinderU(a, z) |
HypergeometricU[Divide[1,2]*a +Divide[1,4], Divide[1,2], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a +Divide[1,4])* Exp[Divide[1,4]*(z)^(2)]*ParabolicCylinderD[-a - 1/2, z] |
Failure | Failure | Fail 5.265954080+2.598925556*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}16.95026320+24.47160682*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}16.95026320-24.47160682*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}5.265954080-2.598925556*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[5.265954078844872, 2.598925568096585] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[16.95026324285485, 24.471606828175403] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[16.95026324285485, -24.471606828175403] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.265954078844872, -2.598925568096585] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}}}{z}\paraU@{a}{z}} | KummerU((1)/(2)*a +(3)/(4), (3)/(2), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a +(3)/(4))*(exp((1)/(4)*(z)^(2)))/(z)*CylinderU(a, z) |
HypergeometricU[Divide[1,2]*a +Divide[3,4], Divide[3,2], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a +Divide[3,4])*Divide[Exp[Divide[1,4]*(z)^(2)],z]*ParabolicCylinderD[-a - 1/2, z] |
Failure | Failure | Fail -4.996298330+.8383991143*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}3.915433252-20.40791018*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}3.915433252+20.40791018*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-4.996298330-.8383991143*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-4.996298332347829, 0.8383991090064162] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[3.9154332288113323, -20.407910193592727] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[3.9154332288113323, 20.407910193592727] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.996298332347829, -0.8383991090064162] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}} = \frac{2^{\frac{1}{2}a-\frac{3}{4}}\EulerGamma@{\tfrac{1}{2}a+\tfrac{3}{4}}e^{\frac{1}{4}z^{2}}}{\sqrt{\pi}}\*\left(\paraU@{a}{z}+\paraU@{a}{-z}\right)} | KummerM((1)/(2)*a +(1)/(4), (1)/(2), (1)/(2)*(z)^(2))=((2)^((1)/(2)*a -(3)/(4))* GAMMA((1)/(2)*a +(3)/(4))*exp((1)/(4)*(z)^(2)))/(sqrt(Pi))*(CylinderU(a, z)+ CylinderU(a, - z)) |
Hypergeometric1F1[Divide[1,2]*a +Divide[1,4], Divide[1,2], Divide[1,2]*(z)^(2)]=Divide[(2)^(Divide[1,2]*a -Divide[3,4])* Gamma[Divide[1,2]*a +Divide[3,4]]*Exp[Divide[1,4]*(z)^(2)],Sqrt[Pi]]*(ParabolicCylinderD[-a - 1/2, z]+ ParabolicCylinderD[-a - 1/2, - z]) |
Successful | Successful | - | - |
| 13.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = \frac{2^{\frac{1}{2}a-\frac{5}{4}}\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{4}}e^{\frac{1}{4}z^{2}}}{z\sqrt{\pi}}\*\left(\paraU@{a}{-z}-\paraU@{a}{z}\right)} | KummerM((1)/(2)*a +(3)/(4), (3)/(2), (1)/(2)*(z)^(2))=((2)^((1)/(2)*a -(5)/(4))* GAMMA((1)/(2)*a +(1)/(4))*exp((1)/(4)*(z)^(2)))/(z*sqrt(Pi))*(CylinderU(a, - z)- CylinderU(a, z)) |
Hypergeometric1F1[Divide[1,2]*a +Divide[3,4], Divide[3,2], Divide[1,2]*(z)^(2)]=Divide[(2)^(Divide[1,2]*a -Divide[5,4])* Gamma[Divide[1,2]*a +Divide[1,4]]*Exp[Divide[1,4]*(z)^(2)],z*Sqrt[Pi]]*(ParabolicCylinderD[-a - 1/2, - z]- ParabolicCylinderD[-a - 1/2, z]) |
Successful | Successful | - | - |
| 13.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{-n}{\tfrac{1}{2}}{z^{2}} = (-1)^{n}\frac{n!}{(2n)!}\HermitepolyH{2n}@{z}} | KummerM(- n, (1)/(2), (z)^(2))=(- 1)^(n)*(factorial(n))/(factorial(2*n))*HermiteH(2*n, z) |
Hypergeometric1F1[- n, Divide[1,2], (z)^(2)]=(- 1)^(n)*Divide[(n)!,(2*n)!]*HermiteH[2*n, z] |
Failure | Failure | Successful | Successful |
| 13.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{-n}{\tfrac{3}{2}}{z^{2}} = (-1)^{n}\frac{n!}{(2n+1)!2z}\HermitepolyH{2n+1}@{z}} | KummerM(- n, (3)/(2), (z)^(2))=(- 1)^(n)*(factorial(n))/(factorial(2*n + 1)*2*z)*HermiteH(2*n + 1, z) |
Hypergeometric1F1[- n, Divide[3,2], (z)^(2)]=(- 1)^(n)*Divide[(n)!,(2*n + 1)!*2*z]*HermiteH[2*n + 1, z] |
Failure | Failure | Successful | Successful |
| 13.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{\tfrac{1}{2}-\tfrac{1}{2}n}{\tfrac{3}{2}}{z^{2}} = 2^{-n}z^{-1}\HermitepolyH{n}@{z}} | KummerU((1)/(2)-(1)/(2)*n, (3)/(2), (z)^(2))= (2)^(- n)* (z)^(- 1)* HermiteH(n, z) |
HypergeometricU[Divide[1,2]-Divide[1,2]*n, Divide[3,2], (z)^(2)]= (2)^(- n)* (z)^(- 1)* HermiteH[n, z] |
Failure | Failure | Fail 2.474873733+3.181980514*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}2.474873733-3.181980514*I <- {z = -2^(1/2)+I*2^(1/2), n = 2} |
Fail
Complex[2.4748737341529163, 3.181980515339464] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.474873734152916, -3.181980515339464] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{-n}{\alpha+1}{z} = (-1)^{n}\Pochhammersym{\alpha+1}{n}\KummerconfhyperM@{-n}{\alpha+1}{z}} | KummerU(- n, alpha + 1, z)=(- 1)^(n)* pochhammer(alpha + 1, n)*KummerM(- n, alpha + 1, z) |
HypergeometricU[- n, \[Alpha]+ 1, z]=(- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*Hypergeometric1F1[- n, \[Alpha]+ 1, z] |
Failure | Failure | Successful | Successful |
| 13.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{-n}{z-n+1}{a} = \Pochhammersym{-z}{n}\KummerconfhyperM@{-n}{z-n+1}{a}} | KummerU(- n, z - n + 1, a)= pochhammer(- z, n)*KummerM(- n, z - n + 1, a) |
HypergeometricU[- n, z - n + 1, a]= Pochhammer[- z, n]*Hypergeometric1F1[- n, z - n + 1, a] |
Failure | Failure | Skip | Successful |
| 13.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = z^{-a}\genhyperF{2}{0}@{a,a-b+1}{-}{-z^{-1}}} | KummerU(a, b, z)= (z)^(- a)* hypergeom([a , a - b + 1], [-], - (z)^(- 1)) |
HypergeometricU[a, b, z]= (z)^(- a)* HypergeometricPFQ[{a , a - b + 1}, {-}, - (z)^(- 1)] |
Error | Failure | - | Error |
| 13.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = z^{-a}\sum_{s=0}^{n-1}\frac{\Pochhammersym{a}{s}\Pochhammersym{a-b+1}{s}}{s!}(-z)^{-s}+\varepsilon_{n}(z)} | KummerU(a, b, z)= (z)^(- a)* sum((pochhammer(a, s)*pochhammer(a - b + 1, s))/(factorial(s))*(- z)^(- s), s = 0..n - 1)+ varepsilon[n]*(z) |
HypergeometricU[a, b, z]= (z)^(- a)* Sum[Divide[Pochhammer[a, s]*Pochhammer[a - b + 1, s],(s)!]*(- z)^(- s), {s, 0, n - 1}]+ Subscript[\[CurlyEpsilon], n]*(z) |
Failure | Failure | Skip | Skip |
| 13.7#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \chi(n) = \sqrt{\pi}\EulerGamma@{\tfrac{1}{2}n+1}/\EulerGamma@{\tfrac{1}{2}n+\tfrac{1}{2}}} | chi*(n)=sqrt(Pi)*GAMMA((1)/(2)*n + 1)/ GAMMA((1)/(2)*n +(1)/(2)) |
\[Chi]*(n)=Sqrt[Pi]*Gamma[Divide[1,2]*n + 1]/ Gamma[Divide[1,2]*n +Divide[1,2]] |
Failure | Failure | Fail -.156582765+1.414213562*I <- {chi = 2^(1/2)+I*2^(1/2), n = 1}.828427124+2.828427124*I <- {chi = 2^(1/2)+I*2^(1/2), n = 2}1.886446196+4.242640686*I <- {chi = 2^(1/2)+I*2^(1/2), n = 3}-.156582765-1.414213562*I <- {chi = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-0.1565827644218014, 1.4142135623730951] <- {Rule[n, 1], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.8284271247461903, 2.8284271247461903] <- {Rule[n, 2], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.8864461969269408, 4.242640687119286] <- {Rule[n, 3], Rule[χ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.1565827644218014, -1.4142135623730951] <- {Rule[n, 1], Rule[χ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.7.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = z^{-a}\sum_{s=0}^{n-1}\frac{\Pochhammersym{a}{s}\Pochhammersym{a-b+1}{s}}{s!}(-z)^{-s}+R_{n}(a,b,z)} | KummerU(a, b, z)= (z)^(- a)* sum((pochhammer(a, s)*pochhammer(a - b + 1, s))/(factorial(s))*(- z)^(- s), s = 0..n - 1)+ R[n]*(a , b , z) |
HypergeometricU[a, b, z]= (z)^(- a)* Sum[Divide[Pochhammer[a, s]*Pochhammer[a - b + 1, s],(s)!]*(- z)^(- s), {s, 0, n - 1}]+ Subscript[R, n]*(a , b , z) |
Failure | Failure | Skip | Error |
| 13.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(e^{t}-1\right)^{a-1}\exp@{t+z(1-e^{-t})} = \sum_{s=0}^{\infty}q_{s}(z,a)t^{s+a-1}} | (exp(t)- 1)^(a - 1)* exp(t + z*(1 - exp(- t)))= sum(q[s]*(z , a)* (t)^(s + a - 1), s = 0..infinity) |
(Exp[t]- 1)^(a - 1)* Exp[t + z*(1 - Exp[- t])]= Sum[Subscript[q, s]*(z , a)* (t)^(s + a - 1), {s, 0, Infinity}] |
Error | Failure | - | Error |
| 13.8#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{k}(z) = \sum_{s=0}^{k}\binom{k}{s}\Pochhammersym{1-b+s}{k-s}z^{s}c_{k+s}(z)} | p[k]*(z)= sum(binomial(k,s)*pochhammer(1 - b + s, k - s)*(z)^(s)* c[k + s]*(z), s = 0..k) |
Subscript[p, k]*(z)= Sum[Binomial[k,s]*Pochhammer[1 - b + s, k - s]*(z)^(s)* Subscript[c, k + s]*(z), {s, 0, k}] |
Failure | Failure | Skip | Skip |
| 13.8#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{k}(z) = \sum_{s=0}^{k}\binom{k}{s}\Pochhammersym{2-b+s}{k-s}z^{s}c_{k+s+1}(z)} | q[k]*(z)= sum(binomial(k,s)*pochhammer(2 - b + s, k - s)*(z)^(s)* c[k + s + 1]*(z), s = 0..k) |
Subscript[q, k]*(z)= Sum[Binomial[k,s]*Pochhammer[2 - b + s, k - s]*(z)^(s)* Subscript[c, k + s + 1]*(z), {s, 0, k}] |
Failure | Failure | Skip | Skip |
| 13.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k+1)c_{k+1}(z)+\sum_{s=0}^{k}\left(\frac{b\BernoullinumberB{s+1}}{(s+1)!}+\frac{z(s+1)\BernoullinumberB{s+2}}{(s+2)!}\right)c_{k-s}(z) = 0} | (k + 1)* c[k + 1]*(z)+ sum(((b*bernoulli(s + 1))/(factorial(s + 1))+(z*(s + 1)* bernoulli(s + 2))/(factorial(s + 2)))* c[k - s]*(z), s = 0..k)= 0 |
(k + 1)* Subscript[c, k + 1]*(z)+ Sum[(Divide[b*BernoulliB[s + 1],(s + 1)!]+Divide[z*(s + 1)* BernoulliB[s + 2],(s + 2)!])* Subscript[c, k - s]*(z), {s, 0, k}]= 0 |
Failure | Failure | Skip | Successful |
| 13.8#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{f}{t} = \left(b\left(\frac{1}{t}-\frac{1}{e^{t}-1}\right)-z\left(\frac{1}{t^{2}}-\frac{e^{t}}{\left(e^{t}-1\right)^{2}}\right)\right)f} | diff(f, t)=(b*((1)/(t)-(1)/(exp(t)- 1))- z*((1)/((t)^(2))-(exp(t))/((exp(t)- 1)^(2))))* f |
D[f, t]=(b*(Divide[1,t]-Divide[1,Exp[t]- 1])- z*(Divide[1,(t)^(2)]-Divide[Exp[t],(Exp[t]- 1)^(2)]))* f |
Failure | Failure | Fail -.3721020438-1.177486994*I <- {b = 2^(1/2)+I*2^(1/2), f = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.1143697985-1.565636569*I <- {b = 2^(1/2)+I*2^(1/2), f = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.5025193734-1.823368814*I <- {b = 2^(1/2)+I*2^(1/2), f = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.7602516187-1.435219239*I <- {b = 2^(1/2)+I*2^(1/2), f = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 13.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \ceiling{-a}} | p*(a , b)= ceil(- a) |
p*(a , b)= Ceiling[- a] |
Failure | Failure | Error | Error |
| 13.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \floor{-\tfrac{1}{2}b}-\floor{-\tfrac{1}{2}(b+1)}} | p*(a , b)= floor(-(1)/(2)*b)- floor(-(1)/(2)*(b + 1)) |
p*(a , b)= Floor[-Divide[1,2]*b]- Floor[-Divide[1,2]*(b + 1)] |
Failure | Failure | Error | Error |
| 13.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \ceiling{-a}-\ceiling{-b}} | p*(a , b)= ceil(- a)- ceil(- b) |
p*(a , b)= Ceiling[- a]- Ceiling[- b] |
Failure | Failure | Skip | Error |
| 13.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}+1\right)}-\floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}\right)}} | p*(a , b)= floor((1)/(2)*(ceil(- b)- ceil(- a)+ 1))- floor((1)/(2)*(ceil(- b)- ceil(- a))) |
p*(a , b)= Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a]+ 1)]- Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a])] |
Failure | Failure | Skip | Error |
| 13.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T(a,b) = \floor{-a}+1} | T*(a , b)= floor(- a)+ 1 |
T*(a , b)= Floor[- a]+ 1 |
Error | Failure | - | Error |
| 13.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T(a,b) = \floor{-a}} | T*(a , b)= floor(- a) |
T*(a , b)= Floor[- a] |
Error | Failure | - | Error |
| 13.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(a,b) = \ceiling{b-a-1}} | P*(a , b)= ceil(b - a - 1) |
P*(a , b)= Ceiling[b - a - 1] |
Failure | Failure | Skip | Error |
| 13.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\OlverconfhyperM@{a}{b}{z}\diff{z} = \frac{1}{a-1}\OlverconfhyperM@{a-1}{b-1}{z}} | int(KummerM(a, b, z)/GAMMA(b), z)=(1)/(a - 1)*KummerM(a - 1, b - 1, z)/GAMMA(b - 1) |
Integrate[Hypergeometric1F1Regularized[a, b, z], z]=Divide[1,a - 1]*Hypergeometric1F1Regularized[a - 1, b - 1, z] |
Successful | Failure | - | Skip |
| 13.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\KummerconfhyperU@{a}{b}{z}\diff{z} = -\frac{1}{a-1}\KummerconfhyperU@{a-1}{b-1}{z}} | int(KummerU(a, b, z), z)= -(1)/(a - 1)*KummerU(a - 1, b - 1, z) |
Integrate[HypergeometricU[a, b, z], z]= -Divide[1,a - 1]*HypergeometricU[a - 1, b - 1, z] |
Successful | Successful | - | - |
| 13.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{b-1}\OlverconfhyperM@{a}{c}{kt}\diff{t} = \EulerGamma@{b}z^{-b}\genhyperOlverF{2}{1}@{a,b}{c}{\ifrac{k}{z}}} | int(exp(- z*t)*(t)^(b - 1)* KummerM(a, c, k*t)/GAMMA(c), t = 0..infinity)= GAMMA(b)*(z)^(- b)* hypergeom([a , b], [c], (k)/(z)) |
Integrate[Exp[- z*t]*(t)^(b - 1)* Hypergeometric1F1Regularized[a, c, k*t], {t, 0, Infinity}]= Gamma[b]*(z)^(- b)* HypergeometricPFQRegularized[{a , b}, {c}, Divide[k,z]] |
Failure | Failure | Skip | Error |
| 13.10.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{b-1}\OlverconfhyperM@{a}{b}{t}\diff{t} = z^{-b}\left(1-\frac{1}{z}\right)^{-a}} | int(exp(- z*t)*(t)^(b - 1)* KummerM(a, b, t)/GAMMA(b), t = 0..infinity)= (z)^(- b)*(1 -(1)/(z))^(- a) |
Integrate[Exp[- z*t]*(t)^(b - 1)* Hypergeometric1F1Regularized[a, b, t], {t, 0, Infinity}]= (z)^(- b)*(1 -Divide[1,z])^(- a) |
Failure | Failure | Skip | Error |
| 13.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-t}t^{b-1}\OlverconfhyperM@{a}{c}{t}\diff{t} = \frac{\EulerGamma@{b}\EulerGamma@{c-a-b}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}} | int(exp(- t)*(t)^(b - 1)* KummerM(a, c, t)/GAMMA(c), t = 0..infinity)=(GAMMA(b)*GAMMA(c - a - b))/(GAMMA(c - a)*GAMMA(c - b)) |
Integrate[Exp[- t]*(t)^(b - 1)* Hypergeometric1F1Regularized[a, c, t], {t, 0, Infinity}]=Divide[Gamma[b]*Gamma[c - a - b],Gamma[c - a]*Gamma[c - b]] |
Failure | Failure | Skip | Error |
| 13.10.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt-t^{2}}t^{2b-2}\OlverconfhyperM@{a}{b}{t^{2}}\diff{t} = \tfrac{1}{2}\pi^{-\frac{1}{2}}\EulerGamma@{b-\tfrac{1}{2}}\KummerconfhyperU@{b-\tfrac{1}{2}}{a+\tfrac{1}{2}}{\tfrac{1}{4}z^{2}}} | int(exp(- z*t - (t)^(2))*(t)^(2*b - 2)* KummerM(a, b, (t)^(2))/GAMMA(b), t = 0..infinity)=(1)/(2)*(Pi)^(-(1)/(2))* GAMMA(b -(1)/(2))*KummerU(b -(1)/(2), a +(1)/(2), (1)/(4)*(z)^(2)) |
Integrate[Exp[- z*t - (t)^(2)]*(t)^(2*b - 2)* Hypergeometric1F1Regularized[a, b, (t)^(2)], {t, 0, Infinity}]=Divide[1,2]*(Pi)^(-Divide[1,2])* Gamma[b -Divide[1,2]]*HypergeometricU[b -Divide[1,2], a +Divide[1,2], Divide[1,4]*(z)^(2)] |
Failure | Failure | Skip | Error |
| 13.10.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{b-1}\KummerconfhyperU@{a}{c}{t}\diff{t} = \EulerGamma@{b}\EulerGamma@{b-c+1}\*z^{-b}\genhyperOlverF{2}{1}@{a,b}{a+b-c+1}{1-\frac{1}{z}}} | int(exp(- z*t)*(t)^(b - 1)* KummerU(a, c, t), t = 0..infinity)= GAMMA(b)*GAMMA(b - c + 1)* (z)^(- b)* hypergeom([a , b], [a + b - c + 1], 1 -(1)/(z)) |
Integrate[Exp[- z*t]*(t)^(b - 1)* HypergeometricU[a, c, t], {t, 0, Infinity}]= Gamma[b]*Gamma[b - c + 1]* (z)^(- b)* HypergeometricPFQRegularized[{a , b}, {a + b - c + 1}, 1 -Divide[1,z]] |
Failure | Failure | Skip | Error |
| 13.10.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi\iunit}\int_{-\infty}^{(0+)}e^{tz}t^{-a}\OlverconfhyperM@{a}{b}{\ifrac{y}{t}}\diff{t} = \frac{1}{\EulerGamma@{a}}z^{\frac{1}{2}(2a-b-1)}y^{\frac{1}{2}(1-b)}\modBesselI{b-1}@{2\sqrt{zy}}} | (1)/(2*Pi*I)*int(exp(t*z)*(t)^(- a)* KummerM(a, b, (y)/(t))/GAMMA(b), t = - infinity..(0 +))=(1)/(GAMMA(a))*(z)^((1)/(2)*(2*a - b - 1))* (y)^((1)/(2)*(1 - b))* BesselI(b - 1, 2*sqrt(z*y)) |
Divide[1,2*Pi*I]*Integrate[Exp[t*z]*(t)^(- a)* Hypergeometric1F1Regularized[a, b, Divide[y,t]], {t, - Infinity, (0 +)}]=Divide[1,Gamma[a]]*(z)^(Divide[1,2]*(2*a - b - 1))* (y)^(Divide[1,2]*(1 - b))* BesselI[b - 1, 2*Sqrt[z*y]] |
Error | Failure | - | Error |
| 13.10.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi\iunit}\int_{-\infty}^{(0+)}e^{tz}t^{-a}\KummerconfhyperU@{a}{b}{\ifrac{y}{t}}\diff{t} = \frac{2z^{\frac{1}{2}(2a-b-1)}y^{\frac{1}{2}(1-b)}}{\EulerGamma@{a}\EulerGamma@{a-b+1}}\modBesselK{b-1}@{2\sqrt{zy}}} | (1)/(2*Pi*I)*int(exp(t*z)*(t)^(- a)* KummerU(a, b, (y)/(t)), t = - infinity..(0 +))=(2*(z)^((1)/(2)*(2*a - b - 1))* (y)^((1)/(2)*(1 - b)))/(GAMMA(a)*GAMMA(a - b + 1))*BesselK(b - 1, 2*sqrt(z*y)) |
Divide[1,2*Pi*I]*Integrate[Exp[t*z]*(t)^(- a)* HypergeometricU[a, b, Divide[y,t]], {t, - Infinity, (0 +)}]=Divide[2*(z)^(Divide[1,2]*(2*a - b - 1))* (y)^(Divide[1,2]*(1 - b)),Gamma[a]*Gamma[a - b + 1]]*BesselK[b - 1, 2*Sqrt[z*y]] |
Error | Failure | - | Error |
| 13.10.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\lambda-1}\OlverconfhyperM@{a}{b}{-t}\diff{t} = \frac{\EulerGamma@{\lambda}\EulerGamma@{a-\lambda}}{\EulerGamma@{a}\EulerGamma@{b-\lambda}}} | int((t)^(lambda - 1)* KummerM(a, b, - t)/GAMMA(b), t = 0..infinity)=(GAMMA(lambda)*GAMMA(a - lambda))/(GAMMA(a)*GAMMA(b - lambda)) |
Integrate[(t)^(\[Lambda]- 1)* Hypergeometric1F1Regularized[a, b, - t], {t, 0, Infinity}]=Divide[Gamma[\[Lambda]]*Gamma[a - \[Lambda]],Gamma[a]*Gamma[b - \[Lambda]]] |
Successful | Failure | - | Error |
| 13.10.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\lambda-1}\KummerconfhyperU@{a}{b}{t}\diff{t} = \frac{\EulerGamma@{\lambda}\EulerGamma@{a-\lambda}\EulerGamma@{\lambda-b+1}}{\EulerGamma@{a}\EulerGamma@{a-b+1}}} | int((t)^(lambda - 1)* KummerU(a, b, t), t = 0..infinity)=(GAMMA(lambda)*GAMMA(a - lambda)*GAMMA(lambda - b + 1))/(GAMMA(a)*GAMMA(a - b + 1)) |
Integrate[(t)^(\[Lambda]- 1)* HypergeometricU[a, b, t], {t, 0, Infinity}]=Divide[Gamma[\[Lambda]]*Gamma[a - \[Lambda]]*Gamma[\[Lambda]- b + 1],Gamma[a]*Gamma[a - b + 1]] |
Successful | Failure | - | Error |
| 13.10.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\cos@{2xt}\OlverconfhyperM@{a}{b}{-t^{2}}\diff{t} = \frac{\sqrt{\pi}}{2\EulerGamma@{a}}x^{2a-1}e^{-x^{2}}\KummerconfhyperU@{b-\tfrac{1}{2}}{a+\tfrac{1}{2}}{x^{2}}} | int(cos(2*x*t)*KummerM(a, b, - (t)^(2))/GAMMA(b), t = 0..infinity)=(sqrt(Pi))/(2*GAMMA(a))*(x)^(2*a - 1)* exp(- (x)^(2))*KummerU(b -(1)/(2), a +(1)/(2), (x)^(2)) |
Integrate[Cos[2*x*t]*Hypergeometric1F1Regularized[a, b, - (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi],2*Gamma[a]]*(x)^(2*a - 1)* Exp[- (x)^(2)]*HypergeometricU[b -Divide[1,2], a +Divide[1,2], (x)^(2)] |
Failure | Failure | Skip | Error |
| 13.10.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-t}t^{b-1-\frac{1}{2}\nu}\OlverconfhyperM@{a}{b}{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = x^{-a+\frac{1}{2}\nu}e^{-x}\OlverconfhyperM@{\nu-b+1}{\nu-a+1}{x}} | int(exp(- t)*(t)^(b - 1 -(1)/(2)*nu)* KummerM(a, b, t)/GAMMA(b)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)= (x)^(- a +(1)/(2)*nu)* exp(- x)*KummerM(nu - b + 1, nu - a + 1, x)/GAMMA(nu - a + 1) |
Integrate[Exp[- t]*(t)^(b - 1 -Divide[1,2]*\[Nu])* Hypergeometric1F1Regularized[a, b, t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]= (x)^(- a +Divide[1,2]*\[Nu])* Exp[- x]*Hypergeometric1F1Regularized[\[Nu]- b + 1, \[Nu]- a + 1, x] |
Failure | Failure | Skip | Error |
| 13.10.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-t}t^{\frac{1}{2}\nu}\OlverconfhyperM@{a}{b}{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{x^{\frac{1}{2}\nu}e^{-x}}{\EulerGamma@{b-a}}\KummerconfhyperU@{a}{a-b+\nu+2}{x}} | int(exp(- t)*(t)^((1)/(2)*nu)* KummerM(a, b, t)/GAMMA(b)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=((x)^((1)/(2)*nu)* exp(- x))/(GAMMA(b - a))*KummerU(a, a - b + nu + 2, x) |
Integrate[Exp[- t]*(t)^(Divide[1,2]*\[Nu])* Hypergeometric1F1Regularized[a, b, t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[(x)^(Divide[1,2]*\[Nu])* Exp[- x],Gamma[b - a]]*HypergeometricU[a, a - b + \[Nu]+ 2, x] |
Failure | Failure | Skip | Error |
| 13.10.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\frac{1}{2}\nu}\KummerconfhyperU@{a}{b}{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{\nu-b+2}}{\EulerGamma@{a}}x^{\frac{1}{2}\nu}\KummerconfhyperU@{\nu-b+2}{\nu-a+2}{x}} | int((t)^((1)/(2)*nu)* KummerU(a, b, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=(GAMMA(nu - b + 2))/(GAMMA(a))*(x)^((1)/(2)*nu)* KummerU(nu - b + 2, nu - a + 2, x) |
Integrate[(t)^(Divide[1,2]*\[Nu])* HypergeometricU[a, b, t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[Gamma[\[Nu]- b + 2],Gamma[a]]*(x)^(Divide[1,2]*\[Nu])* HypergeometricU[\[Nu]- b + 2, \[Nu]- a + 2, x] |
Failure | Failure | Skip | Error |
| 13.10.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-t}t^{\frac{1}{2}\nu}\KummerconfhyperU@{a}{b}{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \EulerGamma@{\nu-b+2}x^{\frac{1}{2}\nu}e^{-x}\OlverconfhyperM@{a}{a-b+\nu+2}{x}} | int(exp(- t)*(t)^((1)/(2)*nu)* KummerU(a, b, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)= GAMMA(nu - b + 2)*(x)^((1)/(2)*nu)* exp(- x)*KummerM(a, a - b + nu + 2, x)/GAMMA(a - b + nu + 2) |
Integrate[Exp[- t]*(t)^(Divide[1,2]*\[Nu])* HypergeometricU[a, b, t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]= Gamma[\[Nu]- b + 2]*(x)^(Divide[1,2]*\[Nu])* Exp[- x]*Hypergeometric1F1Regularized[a, a - b + \[Nu]+ 2, x] |
Failure | Failure | Skip | Error |
| 13.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z} = \EulerGamma@{a-\tfrac{1}{2}}e^{\frac{1}{2}z}\left(\tfrac{1}{4}z\right)^{\frac{1}{2}-a}\*\sum_{s=0}^{\infty}\frac{\Pochhammersym{2a-1}{s}\Pochhammersym{2a-b}{s}}{\Pochhammersym{b}{s}s!}\*\left(a-\tfrac{1}{2}+s\right)\*\modBesselI{a-\frac{1}{2}+s}@{\tfrac{1}{2}z}} | KummerM(a, b, z)= GAMMA(a -(1)/(2))*exp((1)/(2)*z)*((1)/(4)*z)^((1)/(2)- a)* sum((pochhammer(2*a - 1, s)*pochhammer(2*a - b, s))/(pochhammer(b, s)*factorial(s))*(a -(1)/(2)+ s)* BesselI(a -(1)/(2)+ s, (1)/(2)*z), s = 0..infinity) |
Hypergeometric1F1[a, b, z]= Gamma[a -Divide[1,2]]*Exp[Divide[1,2]*z]*(Divide[1,4]*z)^(Divide[1,2]- a)* Sum[Divide[Pochhammer[2*a - 1, s]*Pochhammer[2*a - b, s],Pochhammer[b, s]*(s)!]*(a -Divide[1,2]+ s)* BesselI[a -Divide[1,2]+ s, Divide[1,2]*z], {s, 0, Infinity}] |
Error | Failure | - | Skip |
| 13.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z}\KummerconfhyperM@{-a}{-b}{-z}+\frac{a(a-b)z^{2}}{b^{2}(1-b^{2})}\KummerconfhyperM@{1+a}{2+b}{z}\KummerconfhyperM@{1-a}{2-b}{-z} = 1} | KummerM(a, b, z)*KummerM(- a, - b, - z)+(a*(a - b)* (z)^(2))/((b)^(2)*(1 - (b)^(2)))*KummerM(1 + a, 2 + b, z)*KummerM(1 - a, 2 - b, - z)= 1 |
Hypergeometric1F1[a, b, z]*Hypergeometric1F1[- a, - b, - z]+Divide[a*(a - b)* (z)^(2),(b)^(2)*(1 - (b)^(2))]*Hypergeometric1F1[1 + a, 2 + b, z]*Hypergeometric1F1[1 - a, 2 - b, - z]= 1 |
Failure | Failure | Successful | Skip |
| 13.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{W}{z}+\left(-\frac{1}{4}+\frac{\kappa}{z}+\frac{\frac{1}{4}-\mu^{2}}{z^{2}}\right)W = 0} | diff(W, [z$(2)])+(-(1)/(4)+(kappa)/(z)+((1)/(4)- (mu)^(2))/((z)^(2)))* W = 0 |
D[W, {z, 2}]+(-Divide[1,4]+Divide[\[Kappa],z]+Divide[Divide[1,4]- (\[Mu])^(2),(z)^(2)])* W = 0 |
Failure | Failure | Fail -.2651650428-.4419417382*I <- {W = 2^(1/2)+I*2^(1/2), kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.4419417381+2.563262081*I <- {W = 2^(1/2)+I*2^(1/2), kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-3.093592167-3.270368862*I <- {W = 2^(1/2)+I*2^(1/2), kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}2.386485386-.2651650429*I <- {W = 2^(1/2)+I*2^(1/2), kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.2651650429449553, -0.44194173824159216] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.5632620818012346, 2.3864853865045976] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.2651650429449553, -0.44194173824159216] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.5632620818012346, 2.3864853865045976] <- {Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\KummerconfhyperM@{\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{z}} | WhittakerM(kappa, mu, z)= exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* KummerM((1)/(2)+ mu - kappa, 1 + 2*mu, z) |
WhittakerM[\[Kappa], \[Mu], z]= Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Hypergeometric1F1[Divide[1,2]+ \[Mu]- \[Kappa], 1 + 2*\[Mu], z] |
Successful | Successful | - | - |
| 13.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\KummerconfhyperU@{\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{z}} | WhittakerW(kappa, mu, z)= exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* KummerU((1)/(2)+ mu - kappa, 1 + 2*mu, z) |
WhittakerW[\[Kappa], \[Mu], z]= Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* HypergeometricU[Divide[1,2]+ \[Mu]- \[Kappa], 1 + 2*\[Mu], z] |
Successful | Successful | - | - |
| 13.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperM@{a}{b}{z} = e^{\frac{1}{2}z}z^{-\frac{1}{2}b}\WhittakerconfhyperM{\frac{1}{2}b-a}{\frac{1}{2}b-\frac{1}{2}}@{z}} | KummerM(a, b, z)= exp((1)/(2)*z)*(z)^(-(1)/(2)*b)* WhittakerM((1)/(2)*b - a, (1)/(2)*b -(1)/(2), z) |
Hypergeometric1F1[a, b, z]= Exp[Divide[1,2]*z]*(z)^(-Divide[1,2]*b)* WhittakerM[Divide[1,2]*b - a, Divide[1,2]*b -Divide[1,2], z] |
Successful | Successful | - | - |
| 13.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KummerconfhyperU@{a}{b}{z} = e^{\frac{1}{2}z}z^{-\frac{1}{2}b}\WhittakerconfhyperW{\frac{1}{2}b-a}{\frac{1}{2}b-\frac{1}{2}}@{z}} | KummerU(a, b, z)= exp((1)/(2)*z)*(z)^(-(1)/(2)*b)* WhittakerW((1)/(2)*b - a, (1)/(2)*b -(1)/(2), z) |
HypergeometricU[a, b, z]= Exp[Divide[1,2]*z]*(z)^(-Divide[1,2]*b)* WhittakerW[Divide[1,2]*b - a, Divide[1,2]*b -Divide[1,2], z] |
Successful | Successful | - | - |
| 13.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}z^{s}} | WhittakerM(kappa, mu, z)= exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(z)^(s), s = 0..infinity) |
WhittakerM[\[Kappa], \[Mu], z]= Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Sum[Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(z)^(s), {s, 0, Infinity}] |
Successful | Successful | - | - |
| 13.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{\infty}\frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}z^{s} = z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}\genhyperF{2}{1}@@{-n,\tfrac{1}{2}+\mu-\kappa}{1+2\mu}{2}\frac{\left(-\tfrac{1}{2}z\right)^{n}}{n!}} | exp(-(1)/(2)*z)*(z)^((1)/(2)+ mu)* sum((pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(z)^(s), s = 0..infinity)= (z)^((1)/(2)+ mu)* sum(hypergeom([- n ,(1)/(2)+ mu - kappa], [1 + 2*mu], 2)*((-(1)/(2)*z)^(n))/(factorial(n)), n = 0..infinity) |
Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]+ \[Mu])* Sum[Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(z)^(s), {s, 0, Infinity}]= (z)^(Divide[1,2]+ \[Mu])* Sum[HypergeometricPFQ[{- n ,Divide[1,2]+ \[Mu]- \[Kappa]}, {1 + 2*\[Mu]}, 2]*Divide[(-Divide[1,2]*z)^(n),(n)!], {n, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Pochhammersym{-\frac{1}{2}n-\kappa}{n+1}}{(n+1)!}\WhittakerconfhyperM{\kappa}{\frac{1}{2}(n+1)}@{z} = e^{-\frac{1}{2}z}z^{-\frac{1}{2}n}\sum_{s=n+1}^{\infty}\frac{\Pochhammersym{-\frac{1}{2}n-\kappa}{s}}{\EulerGamma@{s-n}s!}z^{s}} | (pochhammer(-(1)/(2)*n - kappa, n + 1))/(factorial(n + 1))*WhittakerM(kappa, (1)/(2)*(n + 1), z)= exp(-(1)/(2)*z)*(z)^(-(1)/(2)*n)* sum((pochhammer(-(1)/(2)*n - kappa, s))/(GAMMA(s - n)*factorial(s))*(z)^(s), s = n + 1..infinity) |
Divide[Pochhammer[-Divide[1,2]*n - \[Kappa], n + 1],(n + 1)!]*WhittakerM[\[Kappa], Divide[1,2]*(n + 1), z]= Exp[-Divide[1,2]*z]*(z)^(-Divide[1,2]*n)* Sum[Divide[Pochhammer[-Divide[1,2]*n - \[Kappa], s],Gamma[s - n]*(s)!]*(z)^(s), {s, n + 1, Infinity}] |
Successful | Successful | - | - |
| 13.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{ze^{+\pi\iunit}} = +\iunit e^{+\mu\pi\iunit}\WhittakerconfhyperM{-\kappa}{\mu}@{z}} | WhittakerM(kappa, mu, z*exp(+ Pi*I))= + I*exp(+ mu*Pi*I)*WhittakerM(- kappa, mu, z) |
WhittakerM[\[Kappa], \[Mu], z*Exp[+ Pi*I]]= + I*Exp[+ \[Mu]*Pi*I]*WhittakerM[- \[Kappa], \[Mu], z] |
Failure | Failure | Fail -170.7233278-52.66673233*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}5.614866181-.1961391743*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-253.7484615-500.5136150*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}4338.981046-2443.697049*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-170.7233281137989, -52.66673241325771] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-253.74846171929062, -500.51361552060405] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-27.726012706068122, -46.132000771477266] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-52.00289849528395, 25.53895774298251] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{ze^{-\pi\iunit}} = -\iunit e^{-\mu\pi\iunit}\WhittakerconfhyperM{-\kappa}{\mu}@{z}} | WhittakerM(kappa, mu, z*exp(- Pi*I))= - I*exp(- mu*Pi*I)*WhittakerM(- kappa, mu, z) |
WhittakerM[\[Kappa], \[Mu], z*Exp[- Pi*I]]= - I*Exp[- \[Mu]*Pi*I]*WhittakerM[- \[Kappa], \[Mu], z] |
Failure | Failure | Fail -1336.329299+1299.001005*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}4031.109392-3933.985765*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-156.7833633-147.7697510*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}17.75799389-.6206610589*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-1336.3293012153467, 1299.0010073665994] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-156.7833635417097, -147.76975126580453] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.6144703540529446, -5.648276978861849] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[13.567482135419885, 36.936365970710575] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[κ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.14.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{ze^{2m\pi\iunit}} = (-1)^{m}e^{2m\mu\pi\iunit}\WhittakerconfhyperM{\kappa}{\mu}@{z}} | WhittakerM(kappa, mu, z*exp(2*m*Pi*I))=(- 1)^(m)* exp(2*m*mu*Pi*I)*WhittakerM(kappa, mu, z) |
WhittakerM[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]]=(- 1)^(m)* Exp[2*m*\[Mu]*Pi*I]*WhittakerM[\[Kappa], \[Mu], z] |
Failure | Failure | Fail -.1992563118+.7533300151*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}-.1992264798+.7534336021*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-.1992264621+.7534336186*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}5.614866174-.1961391695*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Skip |
| 13.14.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{ze^{2m\pi\iunit}} = \frac{(-1)^{m+1}2\pi\iunit\sin@{2\pi\mu m}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}\EulerGamma@{1+2\mu}\sin@{2\pi\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z}+(-1)^{m}e^{-2m\mu\pi\iunit}\WhittakerconfhyperW{\kappa}{\mu}@{z}} | WhittakerW(kappa, mu, z*exp(2*m*Pi*I))=((- 1)^(m + 1)* 2*Pi*I*sin(2*Pi*mu*m))/(GAMMA((1)/(2)- mu - kappa)*GAMMA(1 + 2*mu)*sin(2*Pi*mu))*WhittakerM(kappa, mu, z)+(- 1)^(m)* exp(- 2*m*mu*Pi*I)*WhittakerW(kappa, mu, z) |
WhittakerW[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]]=Divide[(- 1)^(m + 1)* 2*Pi*I*Sin[2*Pi*\[Mu]*m],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]*Gamma[1 + 2*\[Mu]]*Sin[2*Pi*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]+(- 1)^(m)* Exp[- 2*m*\[Mu]*Pi*I]*WhittakerW[\[Kappa], \[Mu], z] |
Failure | Failure | Fail 4888.973639-5758.546940*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}51701593.85-17588478.17*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}.3859873546e12+.827147997e11*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}339.062648-414.78030*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Skip |
| 13.14.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{m}\WhittakerconfhyperW{\kappa}{\mu}@{ze^{2m\pi\iunit}} = -\frac{e^{2\kappa\pi\iunit}\sin@{2m\mu\pi}+\sin@{(2m-2)\mu\pi}}{\sin@{2\mu\pi}}\WhittakerconfhyperW{\kappa}{\mu}@{z}-\frac{\sin@{2m\mu\pi}2\pi\iunit e^{\kappa\pi\iunit}}{\sin@{2\mu\pi}\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{ze^{\pi\iunit}}} | (- 1)^(m)* WhittakerW(kappa, mu, z*exp(2*m*Pi*I))= -(exp(2*kappa*Pi*I)*sin(2*m*mu*Pi)+ sin((2*m - 2)* mu*Pi))/(sin(2*mu*Pi))*WhittakerW(kappa, mu, z)-(sin(2*m*mu*Pi)*2*Pi*I*exp(kappa*Pi*I))/(sin(2*mu*Pi)*GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*WhittakerW(- kappa, mu, z*exp(Pi*I)) |
(- 1)^(m)* WhittakerW[\[Kappa], \[Mu], z*Exp[2*m*Pi*I]]= -Divide[Exp[2*\[Kappa]*Pi*I]*Sin[2*m*\[Mu]*Pi]+ Sin[(2*m - 2)* \[Mu]*Pi],Sin[2*\[Mu]*Pi]]*WhittakerW[\[Kappa], \[Mu], z]-Divide[Sin[2*m*\[Mu]*Pi]*2*Pi*I*Exp[\[Kappa]*Pi*I],Sin[2*\[Mu]*Pi]*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], z*Exp[Pi*I]] |
Failure | Failure | Fail -.3787433625+.42488234e-1*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}9903.313865-3475.249377*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}-74336427.26-15180270.02*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}-339.0626695+414.7802897*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 1}... skip entries to safe data |
Skip |
| 13.14.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperM{\kappa}{-\mu}@{z}} = -2\mu} | (WhittakerM(kappa, mu, z))*diff(WhittakerM(kappa, - mu, z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerM(kappa, - mu, z))= - 2*mu |
Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerM[\[Kappa], - \[Mu], z]}, z]= - 2*\[Mu] |
Failure | Failure | Successful | Successful |
| 13.14.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{\kappa}{\mu}@{z}} = -\frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}} | (WhittakerM(kappa, mu, z))*diff(WhittakerW(kappa, mu, z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(kappa, mu, z))= -(GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu - kappa)) |
Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[\[Kappa], \[Mu], z]}, z]= -Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]] |
Failure | Failure | Successful | Skip |
| 13.14.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}e^{-(\frac{1}{2}+\mu)\pi\iunit}} | (WhittakerM(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z))=(GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu + kappa))*exp(-((1)/(2)+ mu)* Pi*I) |
Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z]=Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Exp[-(Divide[1,2]+ \[Mu])* Pi*I] |
Failure | Failure | Fail -139.4018328-103.8422707*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-139.4018328-103.8422707*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-34.52500080+37.00315934*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-34.52500081+37.00315938*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 13.14.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}e^{+(\frac{1}{2}+\mu)\pi\iunit}} | (WhittakerM(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerM(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z))=(GAMMA(1 + 2*mu))/(GAMMA((1)/(2)+ mu + kappa))*exp(+((1)/(2)+ mu)* Pi*I) |
Wronskian[{WhittakerM[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z]=Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Exp[+(Divide[1,2]+ \[Mu])* Pi*I] |
Failure | Failure | Fail 139.4018325+103.8422705*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}139.4018324+103.8422705*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}34.52500091-37.00315940*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}34.52500091-37.00315940*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
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| 13.14.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{\kappa}{\mu}@{z}} = -\frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}}} | (WhittakerM(kappa, - mu, z))*diff(WhittakerW(kappa, mu, z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(kappa, mu, z))= -(GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu - kappa)) |
Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[\[Kappa], \[Mu], z]}, z]= -Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]] |
Failure | Failure | Successful | Skip |
| 13.14.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = \frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa}}e^{-(\frac{1}{2}-\mu)\pi\iunit}} | (WhittakerM(kappa, - mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z))=(GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu + kappa))*exp(-((1)/(2)- mu)* Pi*I) |
Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z]=Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]*Exp[-(Divide[1,2]- \[Mu])* Pi*I] |
Failure | Failure | Fail .3494764582e-2+.1012865874*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.3494764522e-2+.1012865875*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}.5639963652+6.066610734*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}.5639963652+6.066610734*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
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| 13.14.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperM{\kappa}{-\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = \frac{\EulerGamma@{1-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa}}e^{+(\frac{1}{2}-\mu)\pi\iunit}} | (WhittakerM(kappa, - mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerM(kappa, - mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z))=(GAMMA(1 - 2*mu))/(GAMMA((1)/(2)- mu + kappa))*exp(+((1)/(2)- mu)* Pi*I) |
Wronskian[{WhittakerM[\[Kappa], - \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z]=Divide[Gamma[1 - 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]]]*Exp[+(Divide[1,2]- \[Mu])* Pi*I] |
Failure | Failure | Fail -.3494764696e-2-.1012865889*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.3494764619e-2-.1012865875*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.5639963688-6.066610726*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-.5639963668-6.066610729*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
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| 13.14.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperW{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} = e^{-\kappa\pi\iunit}} | (WhittakerW(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(+ Pi*I)*z), z)-diff(WhittakerW(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(+ Pi*I)*z))= exp(- kappa*Pi*I) |
Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z]}, z]= Exp[- \[Kappa]*Pi*I] |
Failure | Failure | Fail 22.63381635-81.96203695*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}22.63381635-81.96203695*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}22.63381635-81.96203695*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}22.63381635-81.96203695*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
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| 13.14.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\WhittakerconfhyperW{\kappa}{\mu}@{z},\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} = e^{+\kappa\pi\iunit}} | (WhittakerW(kappa, mu, z))*diff(WhittakerW(- kappa, mu, exp(- Pi*I)*z), z)-diff(WhittakerW(kappa, mu, z), z)*(WhittakerW(- kappa, mu, exp(- Pi*I)*z))= exp(+ kappa*Pi*I) |
Wronskian[{WhittakerW[\[Kappa], \[Mu], z], WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z]}, z]= Exp[+ \[Kappa]*Pi*I] |
Failure | Failure | Fail -22.63381633+81.96203683*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-22.63381632+81.96203679*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-22.63381646+81.96203679*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-22.63381644+81.96203672*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
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| 13.14.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \WhittakerconfhyperW{\kappa}{-\mu}@{z}} | WhittakerW(kappa, mu, z)= WhittakerW(kappa, - mu, z) |
WhittakerW[\[Kappa], \[Mu], z]= WhittakerW[\[Kappa], - \[Mu], z] |
Successful | Successful | - | - |
| 13.14.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{e^{+(\kappa-\mu-\frac{1}{2})\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\kappa}{\mu}@{z}+\frac{e^{+\kappa\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{e^{+\pi\iunit}z}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z)=(exp(+(kappa - mu -(1)/(2))* Pi*I))/(GAMMA((1)/(2)+ mu + kappa))*WhittakerW(kappa, mu, z)+(exp(+ kappa*Pi*I))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerW(- kappa, mu, exp(+ Pi*I)*z) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]=Divide[Exp[+(\[Kappa]- \[Mu]-Divide[1,2])* Pi*I],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[+ \[Kappa]*Pi*I],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], Exp[+ Pi*I]*z] |
Failure | Failure | Fail 1.298497732-.1938713855e-1*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.187122752-1.346515592*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-9.654177833-4.981936798*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}34.26140886+126.3803650*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
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| 13.14.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{e^{-(\kappa-\mu-\frac{1}{2})\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\kappa}{\mu}@{z}+\frac{e^{-\kappa\pi\iunit}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperW{-\kappa}{\mu}@{e^{-\pi\iunit}z}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z)=(exp(-(kappa - mu -(1)/(2))* Pi*I))/(GAMMA((1)/(2)+ mu + kappa))*WhittakerW(kappa, mu, z)+(exp(- kappa*Pi*I))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerW(- kappa, mu, exp(- Pi*I)*z) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]=Divide[Exp[-(\[Kappa]- \[Mu]-Divide[1,2])* Pi*I],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[\[Kappa], \[Mu], z]+Divide[Exp[- \[Kappa]*Pi*I],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerW[- \[Kappa], \[Mu], Exp[- Pi*I]*z] |
Failure | Failure | Fail 579.6433793+324.2736386*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}201.3880428-41.30381202*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-8591.170394-81467.17807*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-198894.9185-2104750.118*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}... skip entries to safe data |
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| 13.14.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{\EulerGamma@{-2\mu}}{\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\WhittakerconfhyperM{\kappa}{\mu}@{z}+\frac{\EulerGamma@{2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\WhittakerconfhyperM{\kappa}{-\mu}@{z}} | WhittakerW(kappa, mu, z)=(GAMMA(- 2*mu))/(GAMMA((1)/(2)- mu - kappa))*WhittakerM(kappa, mu, z)+(GAMMA(2*mu))/(GAMMA((1)/(2)+ mu - kappa))*WhittakerM(kappa, - mu, z) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[Gamma[- 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*WhittakerM[\[Kappa], \[Mu], z]+Divide[Gamma[2*\[Mu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*WhittakerM[\[Kappa], - \[Mu], z] |
Successful | Failure | - | Skip |
| 13.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperM{\kappa-1}{\mu}@{z}+(z-2\kappa)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\WhittakerconfhyperM{\kappa+1}{\mu}@{z} = 0} | (kappa - mu -(1)/(2))* WhittakerM(kappa - 1, mu, z)+(z - 2*kappa)* WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))* WhittakerM(kappa + 1, mu, z)= 0 |
(\[Kappa]- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa]- 1, \[Mu], z]+(z - 2*\[Kappa])* WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])* WhittakerM[\[Kappa]+ 1, \[Mu], z]= 0 |
Successful | Successful | - | - |
| 13.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(z+2\mu)(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | 2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2*mu)*(1 + 2*mu)* WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))*sqrt(z)*WhittakerM(kappa +(1)/(2), mu +(1)/(2), z)= 0 |
2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(z + 2*\[Mu])*(1 + 2*\[Mu])* WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa}{\mu}@{z}-(\kappa+\mu+\tfrac{1}{2})\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | (kappa - mu -(1)/(2))* WhittakerM(kappa -(1)/(2), mu +(1)/(2), z)+(1 + 2*mu)*sqrt(z)*WhittakerM(kappa, mu, z)-(kappa + mu +(1)/(2))* WhittakerM(kappa +(1)/(2), mu +(1)/(2), z)= 0 |
(\[Kappa]- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]+(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa], \[Mu], z]-(\[Kappa]+ \[Mu]+Divide[1,2])* WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-2\mu\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperM{\kappa}{\mu}@{z} = 0} | 2*mu*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)- 2*mu*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)-sqrt(z)*WhittakerM(kappa, mu, z)= 0 |
2*\[Mu]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]- 2*\[Mu]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]-Sqrt[z]*WhittakerM[\[Kappa], \[Mu], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}-2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | 2*mu*(1 + 2*mu)* WhittakerM(kappa, mu, z)- 2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa -(1)/(2), mu -(1)/(2), z)-(kappa - mu -(1)/(2))*sqrt(z)*WhittakerM(kappa -(1)/(2), mu +(1)/(2), z)= 0 |
2*\[Mu]*(1 + 2*\[Mu])* WhittakerM[\[Kappa], \[Mu], z]- 2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}+(z-2\mu)(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | 2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)+(z - 2*mu)*(1 + 2*mu)* WhittakerM(kappa, mu, z)+(kappa - mu -(1)/(2))*sqrt(z)*WhittakerM(kappa -(1)/(2), mu +(1)/(2), z)= 0 |
2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]+(z - 2*\[Mu])*(1 + 2*\[Mu])* WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu(1+2\mu)\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-2\mu(1+2\mu)\WhittakerconfhyperM{\kappa}{\mu}@{z}+(\kappa+\mu+\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperM{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | 2*mu*(1 + 2*mu)*sqrt(z)*WhittakerM(kappa +(1)/(2), mu -(1)/(2), z)- 2*mu*(1 + 2*mu)* WhittakerM(kappa, mu, z)+(kappa + mu +(1)/(2))*sqrt(z)*WhittakerM(kappa +(1)/(2), mu +(1)/(2), z)= 0 |
2*\[Mu]*(1 + 2*\[Mu])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]- 2*\[Mu]*(1 + 2*\[Mu])* WhittakerM[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]+Divide[1,2])*Sqrt[z]*WhittakerM[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Successful |
| 13.15.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | WhittakerW(kappa +(1)/(2), mu +(1)/(2), z)-sqrt(z)*WhittakerW(kappa, mu, z)+(kappa - mu -(1)/(2))* WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)= 0 |
WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]-Sqrt[z]*WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])* WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa+\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0} | WhittakerW(kappa +(1)/(2), mu -(1)/(2), z)-sqrt(z)*WhittakerW(kappa, mu, z)+(kappa + mu -(1)/(2))* WhittakerW(kappa -(1)/(2), mu -(1)/(2), z)= 0 |
WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]-Sqrt[z]*WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]+ \[Mu]-Divide[1,2])* WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\mu\WhittakerconfhyperW{\kappa}{\mu}@{z}-\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0} | 2*mu*WhittakerW(kappa, mu, z)-sqrt(z)*WhittakerW(kappa +(1)/(2), mu +(1)/(2), z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu -(1)/(2), z)= 0 |
2*\[Mu]*WhittakerW[\[Kappa], \[Mu], z]-Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa+1}{\mu}@{z}+(2\kappa-z)\WhittakerconfhyperW{\kappa}{\mu}@{z}+(\kappa-\mu-\tfrac{1}{2})(\kappa+\mu-\tfrac{1}{2})\WhittakerconfhyperW{\kappa-1}{\mu}@{z} = 0} | WhittakerW(kappa + 1, mu, z)+(2*kappa - z)* WhittakerW(kappa, mu, z)+(kappa - mu -(1)/(2))*(kappa + mu -(1)/(2))* WhittakerW(kappa - 1, mu, z)= 0 |
WhittakerW[\[Kappa]+ 1, \[Mu], z]+(2*\[Kappa]- z)* WhittakerW[\[Kappa], \[Mu], z]+(\[Kappa]- \[Mu]-Divide[1,2])*(\[Kappa]+ \[Mu]-Divide[1,2])* WhittakerW[\[Kappa]- 1, \[Mu], z]= 0 |
Successful | Successful | - | - |
| 13.15.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}+2\mu\WhittakerconfhyperW{\kappa}{\mu}@{z}-(\kappa+\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0} | (kappa - mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)+ 2*mu*WhittakerW(kappa, mu, z)-(kappa + mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu -(1)/(2), z)= 0 |
(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]+ 2*\[Mu]*WhittakerW[\[Kappa], \[Mu], z]-(\[Kappa]+ \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\kappa+\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu-\frac{1}{2}}@{z}-(z+2\mu)\WhittakerconfhyperW{\kappa}{\mu}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu+\frac{1}{2}}@{z} = 0} | (kappa + mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu -(1)/(2), z)-(z + 2*mu)* WhittakerW(kappa, mu, z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu +(1)/(2), z)= 0 |
(\[Kappa]+ \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]-Divide[1,2], z]-(z + 2*\[Mu])* WhittakerW[\[Kappa], \[Mu], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]+Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\kappa-\mu-\tfrac{1}{2})\sqrt{z}\WhittakerconfhyperW{\kappa-\frac{1}{2}}{\mu+\frac{1}{2}}@{z}-(z-2\mu)\WhittakerconfhyperW{\kappa}{\mu}@{z}+\sqrt{z}\WhittakerconfhyperW{\kappa+\frac{1}{2}}{\mu-\frac{1}{2}}@{z} = 0} | (kappa - mu -(1)/(2))*sqrt(z)*WhittakerW(kappa -(1)/(2), mu +(1)/(2), z)-(z - 2*mu)* WhittakerW(kappa, mu, z)+sqrt(z)*WhittakerW(kappa +(1)/(2), mu -(1)/(2), z)= 0 |
(\[Kappa]- \[Mu]-Divide[1,2])*Sqrt[z]*WhittakerW[\[Kappa]-Divide[1,2], \[Mu]+Divide[1,2], z]-(z - 2*\[Mu])* WhittakerW[\[Kappa], \[Mu], z]+Sqrt[z]*WhittakerW[\[Kappa]+Divide[1,2], \[Mu]-Divide[1,2], z]= 0 |
Successful | Failure | - | Skip |
| 13.15.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{-2\mu}{n}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa-\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}} | diff(exp((1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer(- 2*mu, n)*exp((1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerM(kappa -(1)/(2)*n, mu -(1)/(2)*n, z) |
D[Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Pochhammer[- 2*\[Mu], n]*Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]-Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \frac{\Pochhammersym{\frac{1}{2}+\mu-\kappa}{n}}{\Pochhammersym{1+2\mu}{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa-\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}} | diff(exp((1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(pochhammer((1)/(2)+ mu - kappa, n))/(pochhammer(1 + 2*mu, n))*exp((1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerM(kappa -(1)/(2)*n, mu +(1)/(2)*n, z) |
D[Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}]=Divide[Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n],Pochhammer[1 + 2*\[Mu], n]]*Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]-Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}e^{\frac{1}{2}z}z^{n-\kappa-1}\WhittakerconfhyperM{\kappa-n}{\mu}@{z}} | (z*diff(z, z))^(n)*(exp((1)/(2)*z)*(z)^(- kappa - 1)* WhittakerM(kappa, mu, z))= pochhammer((1)/(2)+ mu - kappa, n)*exp((1)/(2)*z)*(z)^(n - kappa - 1)* WhittakerM(kappa - n, mu, z) |
(z*D[z, z])^(n)*(Exp[Divide[1,2]*z]*(z)^(- \[Kappa]- 1)* WhittakerM[\[Kappa], \[Mu], z])= Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(n - \[Kappa]- 1)* WhittakerM[\[Kappa]- n, \[Mu], z] |
Failure | Failure | Fail .422889411+.400864309e-1*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}.3423332190-2.928704994*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}28.78460329-27.79294397*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}.8091469094-.1815739427*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.15.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{-2\mu}{n}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperM{\kappa+\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}} | diff(exp(-(1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer(- 2*mu, n)*exp(-(1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerM(kappa +(1)/(2)*n, mu -(1)/(2)*n, z) |
D[Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Pochhammer[- 2*\[Mu], n]*Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]+Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = (-1)^{n}\frac{\Pochhammersym{\frac{1}{2}+\mu+\kappa}{n}}{\Pochhammersym{1+2\mu}{n}}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperM{\kappa+\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}} | diff(exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerM(kappa, mu, z), [z$(n)])=(- 1)^(n)*(pochhammer((1)/(2)+ mu + kappa, n))/(pochhammer(1 + 2*mu, n))*exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerM(kappa +(1)/(2)*n, mu +(1)/(2)*n, z) |
D[Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)*Divide[Pochhammer[Divide[1,2]+ \[Mu]+ \[Kappa], n],Pochhammer[1 + 2*\[Mu], n]]*Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerM[\[Kappa]+Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}\WhittakerconfhyperM{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu+\kappa}{n}e^{-\frac{1}{2}z}z^{\kappa+n-1}\*\WhittakerconfhyperM{\kappa+n}{\mu}@{z}} | (z*diff(z, z))^(n)*(exp(-(1)/(2)*z)*(z)^(kappa - 1)* WhittakerM(kappa, mu, z))= pochhammer((1)/(2)+ mu + kappa, n)*exp(-(1)/(2)*z)*(z)^(kappa + n - 1)* WhittakerM(kappa + n, mu, z) |
(z*D[z, z])^(n)*(Exp[-Divide[1,2]*z]*(z)^(\[Kappa]- 1)* WhittakerM[\[Kappa], \[Mu], z])= Pochhammer[Divide[1,2]+ \[Mu]+ \[Kappa], n]*Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ n - 1)* WhittakerM[\[Kappa]+ n, \[Mu], z] |
Failure | Failure | Fail .3651560696+.5317892033*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-2.267246204+4.379959380*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}-31.10787298-.100038800*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}29.73991513-87.25229264*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.15.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperW{\kappa-\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}} | diff(exp((1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer((1)/(2)+ mu - kappa, n)*exp((1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerW(kappa -(1)/(2)*n, mu +(1)/(2)*n, z) |
D[Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]-Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}\Pochhammersym{\tfrac{1}{2}-\mu-\kappa}{n}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\*\WhittakerconfhyperW{\kappa-\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}} | diff(exp((1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)])=(- 1)^(n)* pochhammer((1)/(2)- mu - kappa, n)*exp((1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerW(kappa -(1)/(2)*n, mu -(1)/(2)*n, z) |
D[Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Pochhammer[Divide[1,2]- \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]-Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(e^{\frac{1}{2}z}z^{-\kappa-1}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = \Pochhammersym{\tfrac{1}{2}+\mu-\kappa}{n}\Pochhammersym{\tfrac{1}{2}-\mu-\kappa}{n}e^{\frac{1}{2}z}z^{n-\kappa-1}\WhittakerconfhyperW{\kappa-n}{\mu}@{z}} | (z*diff(z, z))^(n)*(exp((1)/(2)*z)*(z)^(- kappa - 1)* WhittakerW(kappa, mu, z))= pochhammer((1)/(2)+ mu - kappa, n)*pochhammer((1)/(2)- mu - kappa, n)*exp((1)/(2)*z)*(z)^(n - kappa - 1)* WhittakerW(kappa - n, mu, z) |
(z*D[z, z])^(n)*(Exp[Divide[1,2]*z]*(z)^(- \[Kappa]- 1)* WhittakerW[\[Kappa], \[Mu], z])= Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], n]*Pochhammer[Divide[1,2]- \[Mu]- \[Kappa], n]*Exp[Divide[1,2]*z]*(z)^(n - \[Kappa]- 1)* WhittakerW[\[Kappa]- n, \[Mu], z] |
Failure | Failure | Fail 2.287537999+5.448901962*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}12.33305908+8.582530455*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}22.68496902-17.41418341*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}.1675216432+.4056625244*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.15.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperW{\kappa+\frac{1}{2}n}{\mu+\frac{1}{2}n}@{z}} | diff(exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)])=(- 1)^(n)* exp(-(1)/(2)*z)*(z)^(- mu -(1)/(2)*(n + 1))* WhittakerW(kappa +(1)/(2)*n, mu +(1)/(2)*n, z) |
D[Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(- \[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]+Divide[1,2]*n, \[Mu]+Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\WhittakerconfhyperW{\kappa+\frac{1}{2}n}{\mu-\frac{1}{2}n}@{z}} | diff(exp(-(1)/(2)*z)*(z)^(mu -(1)/(2))* WhittakerW(kappa, mu, z), [z$(n)])=(- 1)^(n)* exp(-(1)/(2)*z)*(z)^(mu -(1)/(2)*(n + 1))* WhittakerW(kappa +(1)/(2)*n, mu -(1)/(2)*n, z) |
D[Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2])* WhittakerW[\[Kappa], \[Mu], z], {z, n}]=(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(\[Mu]-Divide[1,2]*(n + 1))* WhittakerW[\[Kappa]+Divide[1,2]*n, \[Mu]-Divide[1,2]*n, z] |
Failure | Failure | Skip | Skip |
| 13.15.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}\WhittakerconfhyperW{\kappa}{\mu}@{z}\right) = (-1)^{n}e^{-\frac{1}{2}z}z^{\kappa+n-1}\WhittakerconfhyperW{\kappa+n}{\mu}@{z}} | (z*diff(z, z))^(n)*(exp(-(1)/(2)*z)*(z)^(kappa - 1)* WhittakerW(kappa, mu, z))=(- 1)^(n)* exp(-(1)/(2)*z)*(z)^(kappa + n - 1)* WhittakerW(kappa + n, mu, z) |
(z*D[z, z])^(n)*(Exp[-Divide[1,2]*z]*(z)^(\[Kappa]- 1)* WhittakerW[\[Kappa], \[Mu], z])=(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ n - 1)* WhittakerW[\[Kappa]+ n, \[Mu], z] |
Failure | Failure | Fail -.2720350864+.1235096327*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}-1.238205578-.8204474278*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}6.403097481-9.930704107*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}44.88142838-1.79519457*I <- {kappa = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
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| 13.16.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\EulerGamma@{1+2\mu}z^{\mu+\frac{1}{2}}2^{-2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\*\int_{-1}^{1}e^{\frac{1}{2}zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\diff{t}} | WhittakerM(kappa, mu, z)=(GAMMA(1 + 2*mu)*(z)^(mu +(1)/(2))* (2)^(- 2*mu))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)+ mu + kappa))* int(exp((1)/(2)*z*t)*(1 + t)^(mu -(1)/(2)- kappa)*(1 - t)^(mu -(1)/(2)+ kappa), t = - 1..1) |
WhittakerM[\[Kappa], \[Mu], z]=Divide[Gamma[1 + 2*\[Mu]]*(z)^(\[Mu]+Divide[1,2])* (2)^(- 2*\[Mu]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]* Integrate[Exp[Divide[1,2]*z*t]*(1 + t)^(\[Mu]-Divide[1,2]- \[Kappa])*(1 - t)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, - 1, 1}] |
Failure | Failure | Skip | Error |
| 13.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\EulerGamma@{1+2\mu}z^{\lambda}}{\EulerGamma@{1+2\mu-2\lambda}\EulerGamma@{2\lambda}}\*\int_{0}^{1}\WhittakerconfhyperM{\kappa-\lambda}{\mu-\lambda}@{zt}e^{\frac{1}{2}z(t-1)}t^{\mu-\lambda-\frac{1}{2}}{(1-t)^{2\lambda-1}}\diff{t}} | WhittakerM(kappa, mu, z)=(GAMMA(1 + 2*mu)*(z)^(lambda))/(GAMMA(1 + 2*mu - 2*lambda)*GAMMA(2*lambda))* int(WhittakerM(kappa - lambda, mu - lambda, z*t)*exp((1)/(2)*z*(t - 1))*(t)^(mu - lambda -(1)/(2))*(1 - t)^(2*lambda - 1), t = 0..1) |
WhittakerM[\[Kappa], \[Mu], z]=Divide[Gamma[1 + 2*\[Mu]]*(z)^(\[Lambda]),Gamma[1 + 2*\[Mu]- 2*\[Lambda]]*Gamma[2*\[Lambda]]]* Integrate[WhittakerM[\[Kappa]- \[Lambda], \[Mu]- \[Lambda], z*t]*Exp[Divide[1,2]*z*(t - 1)]*(t)^(\[Mu]- \[Lambda]-Divide[1,2])*(1 - t)^(2*\[Lambda]- 1), {t, 0, 1}] |
Failure | Failure | Skip | Error |
| 13.16.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\sqrt{z}e^{\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\int_{0}^{\infty}e^{-t}t^{\kappa-\frac{1}{2}}\BesselJ{2\mu}@{2\sqrt{zt}}\diff{t}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z)=(sqrt(z)*exp((1)/(2)*z))/(GAMMA((1)/(2)+ mu + kappa))*int(exp(- t)*(t)^(kappa -(1)/(2))* BesselJ(2*mu, 2*sqrt(z*t)), t = 0..infinity) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]=Divide[Sqrt[z]*Exp[Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*Integrate[Exp[- t]*(t)^(\[Kappa]-Divide[1,2])* BesselJ[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 13.16.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = \frac{\sqrt{z}e^{-\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}\modBesselI{2\mu}@{2\sqrt{zt}}\diff{t}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z)=(sqrt(z)*exp(-(1)/(2)*z))/(GAMMA((1)/(2)+ mu - kappa))* int(exp(- t)*(t)^(- kappa -(1)/(2))* BesselI(2*mu, 2*sqrt(z*t)), t = 0..infinity) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]=Divide[Sqrt[z]*Exp[-Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Exp[- t]*(t)^(- \[Kappa]-Divide[1,2])* BesselI[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}] |
Failure | Failure | Skip | Successful |
| 13.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{z^{\mu+\frac{1}{2}}2^{-2\mu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{1}^{\infty}e^{-\frac{1}{2}zt}(t-1)^{\mu-\frac{1}{2}-\kappa}(t+1)^{\mu-\frac{1}{2}+\kappa}\diff{t}} | WhittakerW(kappa, mu, z)=((z)^(mu +(1)/(2))* (2)^(- 2*mu))/(GAMMA((1)/(2)+ mu - kappa))* int(exp(-(1)/(2)*z*t)*(t - 1)^(mu -(1)/(2)- kappa)*(t + 1)^(mu -(1)/(2)+ kappa), t = 1..infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[(z)^(\[Mu]+Divide[1,2])* (2)^(- 2*\[Mu]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Exp[-Divide[1,2]*z*t]*(t - 1)^(\[Mu]-Divide[1,2]- \[Kappa])*(t + 1)^(\[Mu]-Divide[1,2]+ \[Kappa]), {t, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 13.16.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{-\frac{1}{2}z}z^{\kappa+1}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}\frac{\WhittakerconfhyperW{-\kappa}{\mu}@{t}e^{-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\diff{t}} | WhittakerW(kappa, mu, z)=(exp(-(1)/(2)*z)*(z)^(kappa + 1))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))* int((WhittakerW(- kappa, mu, t)*exp(-(1)/(2)*t)*(t)^(- kappa - 1))/(t + z), t = 0..infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ 1),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Divide[WhittakerW[- \[Kappa], \[Mu], t]*Exp[-Divide[1,2]*t]*(t)^(- \[Kappa]- 1),t + z], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.16.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{(-1)^{n}e^{-\frac{1}{2}z}z^{\frac{1}{2}-\mu-n}}{\EulerGamma@{1+2\mu}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}\frac{\WhittakerconfhyperM{-\kappa}{\mu}@{t}e^{-\frac{1}{2}t}t^{n+\mu-\frac{1}{2}}}{t+z}\diff{t}} | WhittakerW(kappa, mu, z)=((- 1)^(n)* exp(-(1)/(2)*z)*(z)^((1)/(2)- mu - n))/(GAMMA(1 + 2*mu)*GAMMA((1)/(2)- mu - kappa))* int((WhittakerM(- kappa, mu, t)*exp(-(1)/(2)*t)*(t)^(n + mu -(1)/(2)))/(t + z), t = 0..infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[(- 1)^(n)* Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu]- n),Gamma[1 + 2*\[Mu]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Divide[WhittakerM[- \[Kappa], \[Mu], t]*Exp[-Divide[1,2]*t]*(t)^(n + \[Mu]-Divide[1,2]),t + z], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.16.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{2\sqrt{z}e^{-\frac{1}{2}z}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}\modBesselK{2\mu}@{2\sqrt{zt}}\diff{t}} | WhittakerW(kappa, mu, z)=(2*sqrt(z)*exp(-(1)/(2)*z))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))* int(exp(- t)*(t)^(- kappa -(1)/(2))* BesselK(2*mu, 2*sqrt(z*t)), t = 0..infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[2*Sqrt[z]*Exp[-Divide[1,2]*z],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]* Integrate[Exp[- t]*(t)^(- \[Kappa]-Divide[1,2])* BesselK[2*\[Mu], 2*Sqrt[z*t]], {t, 0, Infinity}] |
Successful | Failure | - | Error |
| 13.16.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = e^{-\frac{1}{2}z}z^{\kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}\genhyperOlverF{2}{1}@@{\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa}{c}{-t}\diff{t}} | WhittakerW(kappa, mu, z)= exp(-(1)/(2)*z)*(z)^(kappa + c)* int(exp(- z*t)*(t)^(c - 1)* hypergeom([(1)/(2)+ mu - kappa ,(1)/(2)- mu - kappa], [c], - t), t = 0..infinity) |
WhittakerW[\[Kappa], \[Mu], z]= Exp[-Divide[1,2]*z]*(z)^(\[Kappa]+ c)* Integrate[Exp[- z*t]*(t)^(c - 1)* HypergeometricPFQRegularized[{Divide[1,2]+ \[Mu]- \[Kappa],Divide[1,2]- \[Mu]- \[Kappa]}, {c}, - t], {t, 0, Infinity}] |
Failure | Failure | Skip | Error |
| 13.16.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{e^{+\pi\iunit}z} = \frac{e^{\frac{1}{2}z+(\frac{1}{2}+\mu)\pi\iunit}}{2\pi\iunit\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{t-\kappa}\EulerGamma@{\frac{1}{2}+\mu-t}}{\EulerGamma@{\frac{1}{2}+\mu+t}}z^{t}\diff{t}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, exp(+ Pi*I)*z)=(exp((1)/(2)*z +((1)/(2)+ mu)* Pi*I))/(2*Pi*I*GAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)*GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))*(z)^(t), t = - I*infinity..I*infinity) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], Exp[+ Pi*I]*z]=Divide[Exp[Divide[1,2]*z +(Divide[1,2]+ \[Mu])* Pi*I],2*Pi*I*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Divide[Gamma[t - \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- t],Gamma[Divide[1,2]+ \[Mu]+ t]]*(z)^(t), {t, - I*Infinity, I*Infinity}] |
Error | Failure | - | Error |
| 13.16.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{e^{-\pi\iunit}z} = \frac{e^{\frac{1}{2}z-(\frac{1}{2}+\mu)\pi\iunit}}{2\pi\iunit\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{t-\kappa}\EulerGamma@{\frac{1}{2}+\mu-t}}{\EulerGamma@{\frac{1}{2}+\mu+t}}z^{t}\diff{t}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, exp(- Pi*I)*z)=(exp((1)/(2)*z -((1)/(2)+ mu)* Pi*I))/(2*Pi*I*GAMMA((1)/(2)+ mu - kappa))* int((GAMMA(t - kappa)*GAMMA((1)/(2)+ mu - t))/(GAMMA((1)/(2)+ mu + t))*(z)^(t), t = - I*infinity..I*infinity) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], Exp[- Pi*I]*z]=Divide[Exp[Divide[1,2]*z -(Divide[1,2]+ \[Mu])* Pi*I],2*Pi*I*Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Integrate[Divide[Gamma[t - \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- t],Gamma[Divide[1,2]+ \[Mu]+ t]]*(z)^(t), {t, - I*Infinity, I*Infinity}] |
Error | Failure | - | Error |
| 13.16.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{-\frac{1}{2}z}}{2\pi\iunit}\*\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{\frac{1}{2}+\mu+t}\EulerGamma@{\frac{1}{2}-\mu+t}\EulerGamma@{-\kappa-t}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}z^{-t}\diff{t}} | WhittakerW(kappa, mu, z)=(exp(-(1)/(2)*z))/(2*Pi*I)* int((GAMMA((1)/(2)+ mu + t)*GAMMA((1)/(2)- mu + t)*GAMMA(- kappa - t))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*(z)^(- t), t = - I*infinity..I*infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[Exp[-Divide[1,2]*z],2*Pi*I]* Integrate[Divide[Gamma[Divide[1,2]+ \[Mu]+ t]*Gamma[Divide[1,2]- \[Mu]+ t]*Gamma[- \[Kappa]- t],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] |
Error | Failure | - | Error |
| 13.16.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\mu}@{z} = \frac{e^{\frac{1}{2}z}}{2\pi\iunit}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{\frac{1}{2}+\mu+t}\EulerGamma@{\frac{1}{2}-\mu+t}}{\EulerGamma@{1-\kappa+t}}z^{-t}\diff{t}} | WhittakerW(kappa, mu, z)=(exp((1)/(2)*z))/(2*Pi*I)*int((GAMMA((1)/(2)+ mu + t)*GAMMA((1)/(2)- mu + t))/(GAMMA(1 - kappa + t))*(z)^(- t), t = - I*infinity..I*infinity) |
WhittakerW[\[Kappa], \[Mu], z]=Divide[Exp[Divide[1,2]*z],2*Pi*I]*Integrate[Divide[Gamma[Divide[1,2]+ \[Mu]+ t]*Gamma[Divide[1,2]- \[Mu]+ t],Gamma[1 - \[Kappa]+ t]]*(z)^(- t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 13.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{0}{\frac{1}{2}}@{2z} = 2\sinh@@{z}} | WhittakerM(0, (1)/(2), 2*z)= 2*sinh(z) |
WhittakerM[0, Divide[1,2], 2*z]= 2*Sinh[z] |
Successful | Successful | - | - |
| 13.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\kappa-\frac{1}{2}}@{z} = \WhittakerconfhyperW{\kappa}{\kappa-\frac{1}{2}}@{z}} | WhittakerM(kappa, kappa -(1)/(2), z)= WhittakerW(kappa, kappa -(1)/(2), z) |
WhittakerM[\[Kappa], \[Kappa]-Divide[1,2], z]= WhittakerW[\[Kappa], \[Kappa]-Divide[1,2], z] |
Successful | Successful | - | - |
| 13.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{\kappa-\frac{1}{2}}@{z} = \WhittakerconfhyperW{\kappa}{-\kappa+\frac{1}{2}}@{z}} | WhittakerW(kappa, kappa -(1)/(2), z)= WhittakerW(kappa, - kappa +(1)/(2), z) |
WhittakerW[\[Kappa], \[Kappa]-Divide[1,2], z]= WhittakerW[\[Kappa], - \[Kappa]+Divide[1,2], z] |
Failure | Successful | Successful | - |
| 13.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\kappa}{-\kappa+\frac{1}{2}}@{z} = e^{-\frac{1}{2}z}z^{\kappa}} | WhittakerW(kappa, - kappa +(1)/(2), z)= exp(-(1)/(2)*z)*(z)^(kappa) |
WhittakerW[\[Kappa], - \[Kappa]+Divide[1,2], z]= Exp[-Divide[1,2]*z]*(z)^(\[Kappa]) |
Failure | Successful | Skip | - |
| 13.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{-\kappa-\frac{1}{2}}@{z} = e^{\frac{1}{2}z}z^{-\kappa}} | WhittakerM(kappa, - kappa -(1)/(2), z)= exp((1)/(2)*z)*(z)^(- kappa) |
WhittakerM[\[Kappa], - \[Kappa]-Divide[1,2], z]= Exp[Divide[1,2]*z]*(z)^(- \[Kappa]) |
Successful | Successful | - | - |
| 13.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\mu-\frac{1}{2}}{\mu}@{z} = 2\mu e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\incgamma@{2\mu}{z}} | WhittakerM(mu -(1)/(2), mu, z)= 2*mu*exp((1)/(2)*z)*(z)^((1)/(2)- mu)* GAMMA(2*mu)-GAMMA(2*mu, z) |
WhittakerM[\[Mu]-Divide[1,2], \[Mu], z]= 2*\[Mu]*Exp[Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu])* Gamma[2*\[Mu], 0, z] |
Failure | Successful | Fail 4.200609167-1.330017252*I <- {mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.614512827-1.289496767*I <- {mu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}2101.588542-3319.229912*I <- {mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-3.931276422-11.62291844*I <- {mu = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
- |
| 13.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\mu-\frac{1}{2}}{\mu}@{z} = e^{\frac{1}{2}z}z^{\frac{1}{2}-\mu}\incGamma@{2\mu}{z}} | WhittakerW(mu -(1)/(2), mu, z)= exp((1)/(2)*z)*(z)^((1)/(2)- mu)* GAMMA(2*mu, z) |
WhittakerW[\[Mu]-Divide[1,2], \[Mu], z]= Exp[Divide[1,2]*z]*(z)^(Divide[1,2]- \[Mu])* Gamma[2*\[Mu], z] |
Successful | Successful | - | - |
| 13.18.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{-\frac{1}{4}}{\frac{1}{4}}@{z^{2}} = \tfrac{1}{2}e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erf@{z}} | WhittakerM(-(1)/(4), (1)/(4), (z)^(2))=(1)/(2)*exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erf(z) |
WhittakerM[-Divide[1,4], Divide[1,4], (z)^(2)]=Divide[1,2]*Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erf[z] |
Failure | Failure | Fail .4198419251+1.807257668*I <- {z = -2^(1/2)-I*2^(1/2)}.4198419251-1.807257668*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.4198419223374512, 1.8072576674879106] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.4198419223374512, -1.8072576674879106] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{-\frac{1}{4}}{+\frac{1}{4}}@{z^{2}} = e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erfc@{z}} | WhittakerW(-(1)/(4), +(1)/(4), (z)^(2))= exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erfc(z) |
WhittakerW[-Divide[1,4], +Divide[1,4], (z)^(2)]= Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erfc[z] |
Failure | Failure | Fail -4.382229868-3.743892002*I <- {z = -2^(1/2)-I*2^(1/2)}-4.382229868+3.743892002*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-4.38222986299419, -3.7438920038513093] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.38222986299419, 3.7438920038513093] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{-\frac{1}{4}}{-\frac{1}{4}}@{z^{2}} = e^{\frac{1}{2}z^{2}}\sqrt{\pi z}\erfc@{z}} | WhittakerW(-(1)/(4), -(1)/(4), (z)^(2))= exp((1)/(2)*(z)^(2))*sqrt(Pi*z)*erfc(z) |
WhittakerW[-Divide[1,4], -Divide[1,4], (z)^(2)]= Exp[Divide[1,2]*(z)^(2)]*Sqrt[Pi*z]*Erfc[z] |
Failure | Failure | Fail -4.382229868-3.743892002*I <- {z = -2^(1/2)-I*2^(1/2)}-4.382229868+3.743892002*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-4.382229862994191, -3.7438920038513093] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-4.382229862994191, 3.7438920038513093] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.18.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{0}{\nu}@{2z} = 2^{2\nu+\frac{1}{2}}\EulerGamma@{1+\nu}\sqrt{z}\modBesselI{\nu}@{z}} | WhittakerM(0, nu, 2*z)= (2)^(2*nu +(1)/(2))* GAMMA(1 + nu)*sqrt(z)*BesselI(nu, z) |
WhittakerM[0, \[Nu], 2*z]= (2)^(2*\[Nu]+Divide[1,2])* Gamma[1 + \[Nu]]*Sqrt[z]*BesselI[\[Nu], z] |
Successful | Successful | - | - |
| 13.18.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{0}{\nu}@{2z} = \sqrt{\ifrac{2z}{\pi}}\modBesselK{\nu}@{z}} | WhittakerW(0, nu, 2*z)=sqrt((2*z)/(Pi))*BesselK(nu, z) |
WhittakerW[0, \[Nu], 2*z]=Sqrt[Divide[2*z,Pi]]*BesselK[\[Nu], z] |
Successful | Successful | - | - |
| 13.18.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{0}{\frac{1}{3}}@{\tfrac{4}{3}z^{\frac{3}{2}}} = 2\sqrt{\pi}z^{\frac{1}{4}}\AiryAi@{z}} | WhittakerW(0, (1)/(3), (4)/(3)*(z)^((3)/(2)))= 2*sqrt(Pi)*(z)^((1)/(4))* AiryAi(z) |
WhittakerW[0, Divide[1,3], Divide[4,3]*(z)^(Divide[3,2])]= 2*Sqrt[Pi]*(z)^(Divide[1,4])* AiryAi[z] |
Failure | Failure | Fail -.111157710+.128876647*I <- {z = -2^(1/2)-I*2^(1/2)}-.111157710-.128876647*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.11115770699234684, 0.12887664550372602] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.11115770699234684, -0.12887664550372602] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 13.18.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{-\frac{1}{2}a}{+\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a}\sqrt{z}\paraU(a,z)} | WhittakerW(-(1)/(2)*a, +(1)/(4), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a)*sqrt(z)*CylinderU(a , z, $1) |
WhittakerW[-Divide[1,2]*a, +Divide[1,4], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a)*Sqrt[z]*ParabolicCylinderD[-a , z - 1/2, $1] |
Error | Error | - | - |
| 13.18.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{-\frac{1}{2}a}{-\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a}\sqrt{z}\paraU(a,z)} | WhittakerW(-(1)/(2)*a, -(1)/(4), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a)*sqrt(z)*CylinderU(a , z, $1) |
WhittakerW[-Divide[1,2]*a, -Divide[1,4], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a)*Sqrt[z]*ParabolicCylinderD[-a , z - 1/2, $1] |
Error | Error | - | - |
| 13.18.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{-\frac{1}{2}a}{-\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a-1}\EulerGamma@{\tfrac{1}{2}a+\tfrac{3}{4}}\sqrt{\ifrac{z}{\pi}}\*\left(\paraU@{a}{z}+\paraU@{a}{-z}\right)} | WhittakerM(-(1)/(2)*a, -(1)/(4), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a - 1)* GAMMA((1)/(2)*a +(3)/(4))*sqrt((z)/(Pi))*(CylinderU(a, z)+ CylinderU(a, - z)) |
WhittakerM[-Divide[1,2]*a, -Divide[1,4], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a - 1)* Gamma[Divide[1,2]*a +Divide[3,4]]*Sqrt[Divide[z,Pi]]*(ParabolicCylinderD[-a - 1/2, z]+ ParabolicCylinderD[-a - 1/2, - z]) |
Failure | Failure | Fail -1.595813139-1.786229512*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-6.548449077-7.324160790*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-6.548449077+7.324160790*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.595813139+1.786229512*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-1.5958131384127743, -1.7862295136979531] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-6.548449089259156, -7.324160795019219] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-6.548449089259156, 7.324160795019219] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5958131384127743, 1.7862295136979531] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.18.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{-\frac{1}{2}a}{\frac{1}{4}}@{\tfrac{1}{2}z^{2}} = 2^{\frac{1}{2}a-2}\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{4}}\sqrt{\ifrac{z}{\pi}}\*\left(\paraU@{a}{-z}-\paraU@{a}{z}\right)} | WhittakerM(-(1)/(2)*a, (1)/(4), (1)/(2)*(z)^(2))= (2)^((1)/(2)*a - 2)* GAMMA((1)/(2)*a +(1)/(4))*sqrt((z)/(Pi))*(CylinderU(a, - z)- CylinderU(a, z)) |
WhittakerM[-Divide[1,2]*a, Divide[1,4], Divide[1,2]*(z)^(2)]= (2)^(Divide[1,2]*a - 2)* Gamma[Divide[1,2]*a +Divide[1,4]]*Sqrt[Divide[z,Pi]]*(ParabolicCylinderD[-a - 1/2, - z]- ParabolicCylinderD[-a - 1/2, z]) |
Failure | Failure | Fail -.2924843841+.9350194047*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}2.175978499-4.464282068*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}2.175978499+4.464282068*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.2924843841-.9350194047*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.29248438571599344, 0.9350194045102764] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.175978498735585, -4.464282074060343] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[2.175978498735585, 4.464282074060343] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.29248438571599344, -0.9350194045102764] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.18.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\frac{1}{4}+n}{-\frac{1}{4}}@{z^{2}} = (-1)^{n}\frac{n!}{(2n)!}e^{-\frac{1}{2}z^{2}}\sqrt{z}\HermitepolyH{2n}@{z}} | WhittakerM((1)/(4)+ n, -(1)/(4), (z)^(2))=(- 1)^(n)*(factorial(n))/(factorial(2*n))*exp(-(1)/(2)*(z)^(2))*sqrt(z)*HermiteH(2*n, z) |
WhittakerM[Divide[1,4]+ n, -Divide[1,4], (z)^(2)]=(- 1)^(n)*Divide[(n)!,(2*n)!]*Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z]*HermiteH[2*n, z] |
Failure | Failure | Fail -10.35742410-12.35814572*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}-51.12520045+7.99947819*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}-70.94025645+106.0858980*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}-10.35742410+12.35814572*I <- {z = -2^(1/2)+I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-10.357424118634546, -12.358145719594317] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-51.125200492418, 7.999478257226418] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-70.9402563798825, 106.08589822655182] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-10.357424118634546, 12.358145719594317] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.18.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\frac{3}{4}+n}{\frac{1}{4}}@{z^{2}} = (-1)^{n}\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}\HermitepolyH{2n+1}@{z}} | WhittakerM((3)/(4)+ n, (1)/(4), (z)^(2))=(- 1)^(n)*(factorial(n))/(factorial(2*n + 1))*(exp(-(1)/(2)*(z)^(2))*sqrt(z))/(2)*HermiteH(2*n + 1, z) |
WhittakerM[Divide[3,4]+ n, Divide[1,4], (z)^(2)]=(- 1)^(n)*Divide[(n)!,(2*n + 1)!]*Divide[Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z],2]*HermiteH[2*n + 1, z] |
Failure | Failure | Fail -10.80554626-3.608039299*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}-20.84223327+13.83655303*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}-10.76427954+47.62458665*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}-10.80554626+3.608039299*I <- {z = -2^(1/2)+I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-10.805546272663701, -3.6080392912358032] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-20.84223327255954, 13.836553078751255] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-10.764279468212877, 47.6245867445262] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-10.805546272663701, 3.6080392912358032] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.18.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\frac{1}{4}+\frac{1}{2}n}{\frac{1}{4}}@{z^{2}} = 2^{-n}e^{-\frac{1}{2}z^{2}}\sqrt{z}\HermitepolyH{n}@{z}} | WhittakerW((1)/(4)+(1)/(2)*n, (1)/(4), (z)^(2))= (2)^(- n)* exp(-(1)/(2)*(z)^(2))*sqrt(z)*HermiteH(n, z) |
WhittakerW[Divide[1,4]+Divide[1,2]*n, Divide[1,4], (z)^(2)]= (2)^(- n)* Exp[-Divide[1,2]*(z)^(2)]*Sqrt[z]*HermiteH[n, z] |
Failure | Failure | Fail -.145985934-3.997335125*I <- {z = -2^(1/2)-I*2^(1/2), n = 1}5.178712051+6.179072864*I <- {z = -2^(1/2)-I*2^(1/2), n = 2}16.20831939+5.412058949*I <- {z = -2^(1/2)-I*2^(1/2), n = 3}-.145985934+3.997335125*I <- {z = -2^(1/2)+I*2^(1/2), n = 1}... skip entries to safe data |
Fail
Complex[-0.1459859378673154, -3.997335125548645] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[5.178712059317274, 6.179072859797158] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[16.208319408995553, 5.412058936853704] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.1459859378673154, 3.997335125548645] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.18.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperW{\frac{1}{2}\alpha+\frac{1}{2}+n}{\frac{1}{2}\alpha}@{z} = (-1)^{n}\Pochhammersym{\alpha+1}{n}\WhittakerconfhyperM{\frac{1}{2}\alpha+\frac{1}{2}+n}{\frac{1}{2}\alpha}@{z}} | WhittakerW((1)/(2)*alpha +(1)/(2)+ n, (1)/(2)*alpha, z)=(- 1)^(n)* pochhammer(alpha + 1, n)*WhittakerM((1)/(2)*alpha +(1)/(2)+ n, (1)/(2)*alpha, z) |
WhittakerW[Divide[1,2]*\[Alpha]+Divide[1,2]+ n, Divide[1,2]*\[Alpha], z]=(- 1)^(n)* Pochhammer[\[Alpha]+ 1, n]*WhittakerM[Divide[1,2]*\[Alpha]+Divide[1,2]+ n, Divide[1,2]*\[Alpha], z] |
Failure | Failure | Successful | Successful |
| 13.20.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta\sqrt{\zeta^{2}+\alpha^{2}}+\alpha^{2}\asinh@{\frac{\zeta}{\alpha}} = \frac{X}{\mu}-\frac{2\kappa}{\mu}\ln@{\frac{X+x-2\kappa}{2\sqrt{\mu^{2}-\kappa^{2}}}}-2\ln@{\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\mu^{2}-\kappa^{2}}}}} | zeta*sqrt((zeta)^(2)+ (alpha)^(2))+ (alpha)^(2)* arcsinh((zeta)/(alpha))=(X)/(mu)-(2*kappa)/(mu)*ln((X + x - 2*kappa)/(2*sqrt((mu)^(2)- (kappa)^(2))))- 2*ln((mu*X + 2*(mu)^(2)- kappa*x)/(x*sqrt((mu)^(2)- (kappa)^(2)))) |
\[zeta]*Sqrt[(\[zeta])^(2)+ (\[Alpha])^(2)]+ (\[Alpha])^(2)* ArcSinh[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]-Divide[2*\[Kappa],\[Mu]]*Log[Divide[X + x - 2*\[Kappa],2*Sqrt[(\[Mu])^(2)- (\[Kappa])^(2)]]]- 2*Log[Divide[\[Mu]*X + 2*(\[Mu])^(2)- \[Kappa]*x,x*Sqrt[(\[Mu])^(2)- (\[Kappa])^(2)]]] |
Failure | Failure | Skip | Error |
| 13.20.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = +\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}} | zeta = +sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu))) |
\[zeta]= +Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]] |
Failure | Failure | Fail .234294656+.8983972080*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}.7206264000+.7915884667*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}1.051794028+.7104212616*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}.234294656-1.930029916*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Error |
| 13.20.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = -\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}} | zeta = -sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu))) |
\[zeta]= -Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]] |
Failure | Failure | Fail 2.594132468+1.930029916*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 1}2.107800724+2.036838657*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 2}1.776633096+2.118005862*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2), x = 3}2.594132468-.8983972080*I <- {mu = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Error |
| 13.20.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta\sqrt{\zeta^{2}-\alpha^{2}}-\alpha^{2}\acosh@{\frac{\zeta}{\alpha}} = \frac{X}{\mu}-\frac{2\kappa}{\mu}\ln@{\frac{X+x-2\kappa}{2\sqrt{\kappa^{2}-\mu^{2}}}}-2\ln@{\frac{\kappa x-\mu X-2\mu^{2}}{x\sqrt{\kappa^{2}-\mu^{2}}}}} | zeta*sqrt((zeta)^(2)- (alpha)^(2))- (alpha)^(2)* arccosh((zeta)/(alpha))=(X)/(mu)-(2*kappa)/(mu)*ln((X + x - 2*kappa)/(2*sqrt((kappa)^(2)- (mu)^(2))))- 2*ln((kappa*x - mu*X - 2*(mu)^(2))/(x*sqrt((kappa)^(2)- (mu)^(2)))) |
\[zeta]*Sqrt[(\[zeta])^(2)- (\[Alpha])^(2)]- (\[Alpha])^(2)* ArcCosh[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]-Divide[2*\[Kappa],\[Mu]]*Log[Divide[X + x - 2*\[Kappa],2*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]- 2*Log[Divide[\[Kappa]*x - \[Mu]*X - 2*(\[Mu])^(2),x*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]] |
Error | Failure | - | Error |
| 13.20.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta\sqrt{\alpha^{2}-\zeta^{2}}+\alpha^{2}\asin@{\frac{\zeta}{\alpha}} = \frac{X}{\mu}+\frac{2\kappa}{\mu}\atan@{\frac{x-2\kappa}{X}}-2\atan@{\frac{\kappa x-2\mu^{2}}{\mu X}}} | zeta*sqrt((alpha)^(2)- (zeta)^(2))+ (alpha)^(2)* arcsin((zeta)/(alpha))=(X)/(mu)+(2*kappa)/(mu)*arctan((x - 2*kappa)/(X))- 2*arctan((kappa*x - 2*(mu)^(2))/(mu*X)) |
\[zeta]*Sqrt[(\[Alpha])^(2)- (\[zeta])^(2)]+ (\[Alpha])^(2)* ArcSin[Divide[\[zeta],\[Alpha]]]=Divide[X,\[Mu]]+Divide[2*\[Kappa],\[Mu]]*ArcTan[Divide[x - 2*\[Kappa],X]]- 2*ArcTan[Divide[\[Kappa]*x - 2*(\[Mu])^(2),\[Mu]*X]] |
Error | Failure | - | Error |
| 13.20.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\zeta\sqrt{\zeta^{2}-\alpha^{2}}-\alpha^{2}\acosh@{-\frac{\zeta}{\alpha}} = -\frac{X}{\mu}+\frac{2\kappa}{\mu}\ln@{\frac{2\kappa-X-x}{2\sqrt{\kappa^{2}-\mu^{2}}}}+2\ln@{\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\kappa^{2}-\mu^{2}}}}} | - zeta*sqrt((zeta)^(2)- (alpha)^(2))- (alpha)^(2)* arccosh(-(zeta)/(alpha))= -(X)/(mu)+(2*kappa)/(mu)*ln((2*kappa - X - x)/(2*sqrt((kappa)^(2)- (mu)^(2))))+ 2*ln((mu*X + 2*(mu)^(2)- kappa*x)/(x*sqrt((kappa)^(2)- (mu)^(2)))) |
- \[zeta]*Sqrt[(\[zeta])^(2)- (\[Alpha])^(2)]- (\[Alpha])^(2)* ArcCosh[-Divide[\[zeta],\[Alpha]]]= -Divide[X,\[Mu]]+Divide[2*\[Kappa],\[Mu]]*Log[Divide[2*\[Kappa]- X - x,2*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]]+ 2*Log[Divide[\[Mu]*X + 2*(\[Mu])^(2)- \[Kappa]*x,x*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]] |
Error | Failure | - | Error |
| 13.21.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\sqrt{\zeta} = \sqrt{x+x^{2}}+\ln@{\sqrt{x}+\sqrt{1+x}}} | 2*sqrt(zeta)=sqrt(x + (x)^(2))+ ln(sqrt(x)+sqrt(1 + x)) |
2*Sqrt[\[zeta]]=Sqrt[x + (x)^(2)]+ Log[Sqrt[x]+Sqrt[1 + x]] |
Failure | Failure | Fail .3175387811+1.082392200*I <- {zeta = 2^(1/2)+I*2^(1/2), x = 1}-.982579648+1.082392200*I <- {zeta = 2^(1/2)+I*2^(1/2), x = 2}-2.167933582+1.082392200*I <- {zeta = 2^(1/2)+I*2^(1/2), x = 3}.3175387811-1.082392200*I <- {zeta = 2^(1/2)-I*2^(1/2), x = 1}... skip entries to safe data |
Error |
| 13.21.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{4\mu^{2}-\kappa\zeta}-\mu\ln@{\frac{2\mu+\sqrt{4\mu^{2}-\kappa\zeta}}{2\mu-\sqrt{4\mu^{2}-\kappa\zeta}}} = \tfrac{1}{2}X+\mu\ln@{\frac{x\sqrt{\kappa^{2}-\mu^{2}}}{2\mu^{2}-\kappa x+\mu X}}+\kappa\ln@{\frac{2\sqrt{\kappa^{2}-\mu^{2}}}{2\kappa-x-X}}} | sqrt(4*(mu)^(2)- kappa*zeta)- mu*ln((2*mu +sqrt(4*(mu)^(2)- kappa*zeta))/(2*mu -sqrt(4*(mu)^(2)- kappa*zeta)))=(1)/(2)*X + mu*ln((x*sqrt((kappa)^(2)- (mu)^(2)))/(2*(mu)^(2)- kappa*x + mu*X))+ kappa*ln((2*sqrt((kappa)^(2)- (mu)^(2)))/(2*kappa - x - X)) |
Sqrt[4*(\[Mu])^(2)- \[Kappa]*\[zeta]]- \[Mu]*Log[Divide[2*\[Mu]+Sqrt[4*(\[Mu])^(2)- \[Kappa]*\[zeta]],2*\[Mu]-Sqrt[4*(\[Mu])^(2)- \[Kappa]*\[zeta]]]]=Divide[1,2]*X + \[Mu]*Log[Divide[x*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)],2*(\[Mu])^(2)- \[Kappa]*x + \[Mu]*X]]+ \[Kappa]*Log[Divide[2*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)],2*\[Kappa]- x - X]] |
Error | Failure | - | Error |
| 13.21.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\kappa\zeta-4\mu^{2}}-2\mu\atan@{\frac{\sqrt{\kappa\zeta-4\mu^{2}}}{2\mu}} = \tfrac{1}{2}(X-\pi\mu)-\mu\atan@{\frac{x\kappa-2\mu^{2}}{\mu X}}+\kappa\asin@{\frac{X}{2\sqrt{\kappa^{2}-\mu^{2}}}}} | sqrt(kappa*zeta - 4*(mu)^(2))- 2*mu*arctan((sqrt(kappa*zeta - 4*(mu)^(2)))/(2*mu))=(1)/(2)*(X - Pi*mu)- mu*arctan((x*kappa - 2*(mu)^(2))/(mu*X))+ kappa*arcsin((X)/(2*sqrt((kappa)^(2)- (mu)^(2)))) |
Sqrt[\[Kappa]*\[zeta]- 4*(\[Mu])^(2)]- 2*\[Mu]*ArcTan[Divide[Sqrt[\[Kappa]*\[zeta]- 4*(\[Mu])^(2)],2*\[Mu]]]=Divide[1,2]*(X - Pi*\[Mu])- \[Mu]*ArcTan[Divide[x*\[Kappa]- 2*(\[Mu])^(2),\[Mu]*X]]+ \[Kappa]*ArcSin[Divide[X,2*Sqrt[(\[Kappa])^(2)- (\[Mu])^(2)]]] |
Error | Failure | - | Error |
| 13.23.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{\nu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\mu+\nu+\tfrac{1}{2}}}{\left(z+\frac{1}{2}\right)^{\mu+\nu+\frac{1}{2}}}\*\genhyperF{2}{1}@@{\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}+\mu+\nu}{1+2\mu}{\frac{1}{z+\frac{1}{2}}}} | int(exp(- z*t)*(t)^(nu - 1)* WhittakerM(kappa, mu, t), t = 0..infinity)=(GAMMA(mu + nu +(1)/(2)))/((z +(1)/(2))^(mu + nu +(1)/(2)))* hypergeom([(1)/(2)+ mu - kappa ,(1)/(2)+ mu + nu], [1 + 2*mu], (1)/(z +(1)/(2))) |
Integrate[Exp[- z*t]*(t)^(\[Nu]- 1)* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}]=Divide[Gamma[\[Mu]+ \[Nu]+Divide[1,2]],(z +Divide[1,2])^(\[Mu]+ \[Nu]+Divide[1,2])]* HypergeometricPFQ[{Divide[1,2]+ \[Mu]- \[Kappa],Divide[1,2]+ \[Mu]+ \[Nu]}, {1 + 2*\[Mu]}, Divide[1,z +Divide[1,2]]] |
Failure | Failure | Skip | Error |
| 13.23.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{\mu-\frac{1}{2}}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \EulerGamma@{2\mu+1}\left(z+\tfrac{1}{2}\right)^{-\kappa-\mu-\frac{1}{2}}\*\left(z-\tfrac{1}{2}\right)^{\kappa-\mu-\frac{1}{2}}} | int(exp(- z*t)*(t)^(mu -(1)/(2))* WhittakerM(kappa, mu, t), t = 0..infinity)= GAMMA(2*mu + 1)*(z +(1)/(2))^(- kappa - mu -(1)/(2))*(z -(1)/(2))^(kappa - mu -(1)/(2)) |
Integrate[Exp[- z*t]*(t)^(\[Mu]-Divide[1,2])* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}]= Gamma[2*\[Mu]+ 1]*(z +Divide[1,2])^(- \[Kappa]- \[Mu]-Divide[1,2])*(z -Divide[1,2])^(\[Kappa]- \[Mu]-Divide[1,2]) |
Failure | Failure | Skip | Error |
| 13.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\nu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\mu+\nu+\frac{1}{2}}\EulerGamma@{\kappa-\nu}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}\EulerGamma@{\frac{1}{2}+\mu-\nu}}} | (1)/(GAMMA(1 + 2*mu))*int(exp(-(1)/(2)*t)*(t)^(nu - 1)* WhittakerM(kappa, mu, t), t = 0..infinity)=(GAMMA(mu + nu +(1)/(2))*GAMMA(kappa - nu))/(GAMMA((1)/(2)+ mu + kappa)*GAMMA((1)/(2)+ mu - nu)) |
Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Exp[-Divide[1,2]*t]*(t)^(\[Nu]- 1)* WhittakerM[\[Kappa], \[Mu], t], {t, 0, Infinity}]=Divide[Gamma[\[Mu]+ \[Nu]+Divide[1,2]]*Gamma[\[Kappa]- \[Nu]],Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]*Gamma[Divide[1,2]+ \[Mu]- \[Nu]]] |
Failure | Failure | Skip | Error |
| 13.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{\nu-1}\WhittakerconfhyperW{\kappa}{\mu}@{t}\diff{t} = \EulerGamma@{\tfrac{1}{2}+\mu+\nu}\EulerGamma@{\tfrac{1}{2}-\mu+\nu}\*\genhyperOlverF{2}{1}@@{\tfrac{1}{2}-\mu+\nu,\tfrac{1}{2}+\mu+\nu}{\nu-\kappa+1}{\tfrac{1}{2}-z}} | int(exp(- z*t)*(t)^(nu - 1)* WhittakerW(kappa, mu, t), t = 0..infinity)= GAMMA((1)/(2)+ mu + nu)*GAMMA((1)/(2)- mu + nu)* hypergeom([(1)/(2)- mu + nu ,(1)/(2)+ mu + nu], [nu - kappa + 1], (1)/(2)- z) |
Integrate[Exp[- z*t]*(t)^(\[Nu]- 1)* WhittakerW[\[Kappa], \[Mu], t], {t, 0, Infinity}]= Gamma[Divide[1,2]+ \[Mu]+ \[Nu]]*Gamma[Divide[1,2]- \[Mu]+ \[Nu]]* HypergeometricPFQRegularized[{Divide[1,2]- \[Mu]+ \[Nu],Divide[1,2]+ \[Mu]+ \[Nu]}, {\[Nu]- \[Kappa]+ 1}, Divide[1,2]- z] |
Failure | Failure | Skip | Error |
| 13.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{\frac{1}{2}t}t^{\nu-1}\WhittakerconfhyperW{\kappa}{\mu}@{t}\diff{t} = \frac{\EulerGamma@{\frac{1}{2}+\mu+\nu}\EulerGamma@{\frac{1}{2}-\mu+\nu}\EulerGamma@{-\kappa-\nu}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}} | int(exp((1)/(2)*t)*(t)^(nu - 1)* WhittakerW(kappa, mu, t), t = 0..infinity)=(GAMMA((1)/(2)+ mu + nu)*GAMMA((1)/(2)- mu + nu)*GAMMA(- kappa - nu))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa)) |
Integrate[Exp[Divide[1,2]*t]*(t)^(\[Nu]- 1)* WhittakerW[\[Kappa], \[Mu], t], {t, 0, Infinity}]=Divide[Gamma[Divide[1,2]+ \[Mu]+ \[Nu]]*Gamma[Divide[1,2]- \[Mu]+ \[Nu]]*Gamma[- \[Kappa]- \[Nu]],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]] |
Failure | Failure | Skip | Error |
| 13.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}2\pi\iunit}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}\WhittakerconfhyperM{\kappa}{\mu}@{t^{-1}}\diff{t} = \frac{z^{-\kappa-\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\modBesselI{2\mu}@{2\sqrt{z}}} | (1)/(GAMMA(1 + 2*mu)*2*Pi*I)*int(exp(z*t +(1)/(2)*(t)^(- 1))*(t)^(kappa)* WhittakerM(kappa, mu, (t)^(- 1)), t = - infinity..(0 +))=((z)^(- kappa -(1)/(2)))/(GAMMA((1)/(2)+ mu - kappa))*BesselI(2*mu, 2*sqrt(z)) |
Divide[1,Gamma[1 + 2*\[Mu]]*2*Pi*I]*Integrate[Exp[z*t +Divide[1,2]*(t)^(- 1)]*(t)^(\[Kappa])* WhittakerM[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}]=Divide[(z)^(- \[Kappa]-Divide[1,2]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]*BesselI[2*\[Mu], 2*Sqrt[z]] |
Error | Failure | - | Error |
| 13.23.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2\pi\iunit}\int_{-\infty}^{(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}\WhittakerconfhyperW{\kappa}{\mu}@{t^{-1}}\diff{t} = \frac{2z^{-\kappa-\frac{1}{2}}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}\EulerGamma@{\frac{1}{2}-\mu-\kappa}}\modBesselK{2\mu}@{2\sqrt{z}}} | (1)/(2*Pi*I)*int(exp(z*t +(1)/(2)*(t)^(- 1))*(t)^(kappa)* WhittakerW(kappa, mu, (t)^(- 1)), t = - infinity..(0 +))=(2*(z)^(- kappa -(1)/(2)))/(GAMMA((1)/(2)+ mu - kappa)*GAMMA((1)/(2)- mu - kappa))*BesselK(2*mu, 2*sqrt(z)) |
Divide[1,2*Pi*I]*Integrate[Exp[z*t +Divide[1,2]*(t)^(- 1)]*(t)^(\[Kappa])* WhittakerW[\[Kappa], \[Mu], (t)^(- 1)], {t, - Infinity, (0 +)}]=Divide[2*(z)^(- \[Kappa]-Divide[1,2]),Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]*Gamma[Divide[1,2]- \[Mu]- \[Kappa]]]*BesselK[2*\[Mu], 2*Sqrt[z]] |
Error | Failure | - | Error |
| 13.23.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}\cos@{2xt}e^{-\frac{1}{2}t^{2}}t^{-2\mu-1}\WhittakerconfhyperM{\kappa}{\mu}@{t^{2}}\diff{t} = \frac{\sqrt{\pi}e^{-\frac{1}{2}x^{2}}x^{\mu+\kappa-1}}{2\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\WhittakerconfhyperW{\frac{1}{2}\kappa-\frac{3}{2}\mu}{\frac{1}{2}\kappa+\frac{1}{2}\mu}@{x^{2}}} | (1)/(GAMMA(1 + 2*mu))*int(cos(2*x*t)*exp(-(1)/(2)*(t)^(2))*(t)^(- 2*mu - 1)* WhittakerM(kappa, mu, (t)^(2)), t = 0..infinity)=(sqrt(Pi)*exp(-(1)/(2)*(x)^(2))*(x)^(mu + kappa - 1))/(2*GAMMA((1)/(2)+ mu + kappa))*WhittakerW((1)/(2)*kappa -(3)/(2)*mu, (1)/(2)*kappa +(1)/(2)*mu, (x)^(2)) |
Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Cos[2*x*t]*Exp[-Divide[1,2]*(t)^(2)]*(t)^(- 2*\[Mu]- 1)* WhittakerM[\[Kappa], \[Mu], (t)^(2)], {t, 0, Infinity}]=Divide[Sqrt[Pi]*Exp[-Divide[1,2]*(x)^(2)]*(x)^(\[Mu]+ \[Kappa]- 1),2*Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]*WhittakerW[Divide[1,2]*\[Kappa]-Divide[3,2]*\[Mu], Divide[1,2]*\[Kappa]+Divide[1,2]*\[Mu], (x)^(2)] |
Failure | Failure | Skip | Error |
| 13.23.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\mu-\frac{1}{2}(\nu+1)}\WhittakerconfhyperM{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa+\nu}}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa-\mu-\frac{3}{2})}\*\WhittakerconfhyperM{\frac{1}{2}(\kappa+3\mu-\nu+\frac{1}{2})}{\frac{1}{2}(\kappa-\mu+\nu-\frac{1}{2})}@{x}} | int(exp(-(1)/(2)*t)*(t)^(mu -(1)/(2)*(nu + 1))* WhittakerM(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=(GAMMA(1 + 2*mu))/(GAMMA((1)/(2)- mu + kappa + nu))* exp(-(1)/(2)*x)*(x)^((1)/(2)*(kappa - mu -(3)/(2)))* WhittakerM((1)/(2)*(kappa + 3*mu - nu +(1)/(2)), (1)/(2)*(kappa - mu + nu -(1)/(2)), x) |
Integrate[Exp[-Divide[1,2]*t]*(t)^(\[Mu]-Divide[1,2]*(\[Nu]+ 1))* WhittakerM[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[Gamma[1 + 2*\[Mu]],Gamma[Divide[1,2]- \[Mu]+ \[Kappa]+ \[Nu]]]* Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Kappa]- \[Mu]-Divide[3,2]))* WhittakerM[Divide[1,2]*(\[Kappa]+ 3*\[Mu]- \[Nu]+Divide[1,2]), Divide[1,2]*(\[Kappa]- \[Mu]+ \[Nu]-Divide[1,2]), x] |
Failure | Failure | Skip | Error |
| 13.23.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperM{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa+\mu-\frac{3}{2})}}{\EulerGamma@{\frac{1}{2}+\mu+\kappa}}\*\WhittakerconfhyperW{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2})}{\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2})}@{x}} | (1)/(GAMMA(1 + 2*mu))*int(exp(-(1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerM(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=(exp(-(1)/(2)*x)*(x)^((1)/(2)*(kappa + mu -(3)/(2))))/(GAMMA((1)/(2)+ mu + kappa))* WhittakerW((1)/(2)*(kappa - 3*mu + nu +(1)/(2)), (1)/(2)*(kappa + mu - nu -(1)/(2)), x) |
Divide[1,Gamma[1 + 2*\[Mu]]]*Integrate[Exp[-Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerM[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Kappa]+ \[Mu]-Divide[3,2])),Gamma[Divide[1,2]+ \[Mu]+ \[Kappa]]]* WhittakerW[Divide[1,2]*(\[Kappa]- 3*\[Mu]+ \[Nu]+Divide[1,2]), Divide[1,2]*(\[Kappa]+ \[Mu]- \[Nu]-Divide[1,2]), x] |
Failure | Failure | Skip | Error |
| 13.23.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperW{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{\nu-2\mu+1}}{\EulerGamma@{\frac{1}{2}+\mu-\kappa}}\*e^{\frac{1}{2}x}x^{\frac{1}{2}(\mu-\kappa-\frac{3}{2})}\*\WhittakerconfhyperW{\frac{1}{2}(\kappa+3\mu-\nu-\frac{1}{2})}{\frac{1}{2}(\kappa-\mu+\nu+\frac{1}{2})}@{x}} | int(exp((1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerW(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=(GAMMA(nu - 2*mu + 1))/(GAMMA((1)/(2)+ mu - kappa))* exp((1)/(2)*x)*(x)^((1)/(2)*(mu - kappa -(3)/(2)))* WhittakerW((1)/(2)*(kappa + 3*mu - nu -(1)/(2)), (1)/(2)*(kappa - mu + nu +(1)/(2)), x) |
Integrate[Exp[Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerW[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[Gamma[\[Nu]- 2*\[Mu]+ 1],Gamma[Divide[1,2]+ \[Mu]- \[Kappa]]]* Exp[Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Mu]- \[Kappa]-Divide[3,2]))* WhittakerW[Divide[1,2]*(\[Kappa]+ 3*\[Mu]- \[Nu]-Divide[1,2]), Divide[1,2]*(\[Kappa]- \[Mu]+ \[Nu]+Divide[1,2]), x] |
Failure | Failure | Skip | Error |
| 13.23.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}\WhittakerconfhyperW{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t} = \frac{\EulerGamma@{\nu-2\mu+1}}{\EulerGamma@{\frac{3}{2}-\mu-\kappa+\nu}}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\mu+\kappa-\frac{3}{2})}\*\WhittakerconfhyperM{\frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2})}{\frac{1}{2}(\nu-\mu-\kappa+\frac{1}{2})}@{x}} | int(exp(-(1)/(2)*t)*(t)^((1)/(2)*(nu - 1)- mu)* WhittakerW(kappa, mu, t)*BesselJ(nu, 2*sqrt(x*t)), t = 0..infinity)=(GAMMA(nu - 2*mu + 1))/(GAMMA((3)/(2)- mu - kappa + nu))* exp(-(1)/(2)*x)*(x)^((1)/(2)*(mu + kappa -(3)/(2)))* WhittakerM((1)/(2)*(kappa - 3*mu + nu +(1)/(2)), (1)/(2)*(nu - mu - kappa +(1)/(2)), x) |
Integrate[Exp[-Divide[1,2]*t]*(t)^(Divide[1,2]*(\[Nu]- 1)- \[Mu])* WhittakerW[\[Kappa], \[Mu], t]*BesselJ[\[Nu], 2*Sqrt[x*t]], {t, 0, Infinity}]=Divide[Gamma[\[Nu]- 2*\[Mu]+ 1],Gamma[Divide[3,2]- \[Mu]- \[Kappa]+ \[Nu]]]* Exp[-Divide[1,2]*x]*(x)^(Divide[1,2]*(\[Mu]+ \[Kappa]-Divide[3,2]))* WhittakerM[Divide[1,2]*(\[Kappa]- 3*\[Mu]+ \[Nu]+Divide[1,2]), Divide[1,2]*(\[Nu]- \[Mu]- \[Kappa]+Divide[1,2]), x] |
Failure | Failure | Skip | Error |
| 13.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z} = \EulerGamma@{\kappa+\mu}2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{\infty}(-1)^{s}\frac{\Pochhammersym{2\kappa+2\mu}{s}\Pochhammersym{2\kappa}{s}}{\Pochhammersym{1+2\mu}{s}s!}\*\left(\kappa+\mu+s\right)\modBesselI{\kappa+\mu+s}@{\tfrac{1}{2}z}} | WhittakerM(kappa, mu, z)= GAMMA(kappa + mu)*(2)^(2*kappa + 2*mu)* (z)^((1)/(2)- kappa)* sum((- 1)^(s)*(pochhammer(2*kappa + 2*mu, s)*pochhammer(2*kappa, s))/(pochhammer(1 + 2*mu, s)*factorial(s))*(kappa + mu + s)* BesselI(kappa + mu + s, (1)/(2)*z), s = 0..infinity) |
WhittakerM[\[Kappa], \[Mu], z]= Gamma[\[Kappa]+ \[Mu]]*(2)^(2*\[Kappa]+ 2*\[Mu])* (z)^(Divide[1,2]- \[Kappa])* Sum[(- 1)^(s)*Divide[Pochhammer[2*\[Kappa]+ 2*\[Mu], s]*Pochhammer[2*\[Kappa], s],Pochhammer[1 + 2*\[Mu], s]*(s)!]*(\[Kappa]+ \[Mu]+ s)* BesselI[\[Kappa]+ \[Mu]+ s, Divide[1,2]*z], {s, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.24.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\EulerGamma@{1+2\mu}}\WhittakerconfhyperM{\kappa}{\mu}@{z} = 2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(2\sqrt{\kappa z}\right)^{-2\mu-s}\BesselJ{2\mu+s}@{2\sqrt{\kappa z}}} | (1)/(GAMMA(1 + 2*mu))*WhittakerM(kappa, mu, z)= (2)^(2*mu)* sum(p(p[s])^(mu)*(z)*(2*sqrt(kappa*z))^(- 2*mu - s)* BesselJ(2*mu + s, 2*sqrt(kappa*z)), s = 0..infinity) |
Divide[1,Gamma[1 + 2*\[Mu]]]*WhittakerM[\[Kappa], \[Mu], z]= (2)^(2*\[Mu])* Sum[p(Subscript[p, s])^(\[Mu])*(z)*(2*Sqrt[\[Kappa]*z])^(- 2*\[Mu]- s)* BesselJ[2*\[Mu]+ s, 2*Sqrt[\[Kappa]*z]], {s, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@{-\tfrac{1}{2}z\left(\coth@@{t}-\frac{1}{t}\right)}\left(\frac{t}{\sinh@@{t}}\right)^{1-2\mu} = \sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)\left(-\frac{t}{z}\right)^{s}} | exp(-(1)/(2)*z*(coth(t)-(1)/(t)))*((t)/(sinh(t)))^(1 - 2*mu)sum(p(p[s])^(mu)*(z)*(-(t)/(z))^(s), s = 0..infinity) |
Exp[-Divide[1,2]*z*(Coth[t]-Divide[1,t])]*(Divide[t,Sinh[t]])^(1 - 2*\[Mu])Sum[p(Subscript[p, s])^(\[Mu])*(z)*(-Divide[t,z])^(s), {s, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.25.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{z}\WhittakerconfhyperM{\kappa}{-\mu-1}@{z}+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}\WhittakerconfhyperM{\kappa}{\mu+1}@{z}\WhittakerconfhyperM{\kappa}{-\mu}@{z} = 1} | WhittakerM(kappa, mu, z)*WhittakerM(kappa, - mu - 1, z)+(((1)/(2)+ mu + kappa)*((1)/(2)+ mu - kappa))/(4*mu*(1 + mu)*(1 + 2*mu)^(2))*WhittakerM(kappa, mu + 1, z)*WhittakerM(kappa, - mu, z)= 1 |
WhittakerM[\[Kappa], \[Mu], z]*WhittakerM[\[Kappa], - \[Mu]- 1, z]+Divide[(Divide[1,2]+ \[Mu]+ \[Kappa])*(Divide[1,2]+ \[Mu]- \[Kappa]),4*\[Mu]*(1 + \[Mu])*(1 + 2*\[Mu])^(2)]*WhittakerM[\[Kappa], \[Mu]+ 1, z]*WhittakerM[\[Kappa], - \[Mu], z]= 1 |
Failure | Failure | Successful | Successful |
| 13.28#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(\xi) = \xi^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(1)}(2\iunit k\xi)} | f[1]*(xi)= (xi)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(1)*(2*I*k*xi) |
Subscript[f, 1]*(\[Xi])= (\[Xi])^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(1)*(2*I*k*\[Xi]) |
Failure | Failure | Fail 5.226251858+1.835215598*I <- {xi = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[1] = 2^(1/2)+I*2^(1/2), k = 1}10.45250372-.329568802*I <- {xi = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[1] = 2^(1/2)+I*2^(1/2), k = 2}15.67875557-2.494353202*I <- {xi = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[1] = 2^(1/2)+I*2^(1/2), k = 3}9.226251856-2.164784400*I <- {xi = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[1] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[5.226251859505505, 1.8352155994152124] <- {Rule[k, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.45250371901101, -0.3295688011695752] <- {Rule[k, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[15.678755578516517, -2.4943532017543637] <- {Rule[k, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-2.164784400584788, -1.2262518595055054] <- {Rule[k, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.28#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(\eta) = \eta^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(2)}(-2\iunit k\eta)} | f[2]*(eta)= (eta)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(2)*(- 2*I*k*eta) |
Subscript[f, 2]*(\[Eta])= (\[Eta])^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(2)*(- 2*I*k*\[Eta]) |
Failure | Failure | Fail -10.45250371-.329568800*I <- {eta = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), k = 1}-20.90500742-4.659137598*I <- {eta = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), k = 2}-31.35751114-8.988706392*I <- {eta = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), k = 3}-6.452503712-4.329568798*I <- {eta = 2^(1/2)+I*2^(1/2), V[kappa,1/2*p] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Fail
Complex[-10.45250371901101, -0.3295688011695752] <- {Rule[k, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-20.90500743802202, -4.65913760233915] <- {Rule[k, 2], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-31.35751115703303, -8.988706403508727] <- {Rule[k, 3], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[10.45250371901101, 8.329568801169575] <- {Rule[k, 1], Rule[η, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 13.29.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{2}z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{2\mu}{s}\Pochhammersym{\frac{1}{2}+\mu-\kappa}{s}}{\Pochhammersym{2\mu}{2s}s!}(-z)^{s}y(s)} | exp(-(1)/(2)*z)= sum((pochhammer(2*mu, s)*pochhammer((1)/(2)+ mu - kappa, s))/(pochhammer(2*mu, 2*s)*factorial(s))*(- z)^(s)* y*(s), s = 0..infinity) |
Exp[-Divide[1,2]*z]= Sum[Divide[Pochhammer[2*\[Mu], s]*Pochhammer[Divide[1,2]+ \[Mu]- \[Kappa], s],Pochhammer[2*\[Mu], 2*s]*(s)!]*(- z)^(s)* y*(s), {s, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.29.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(n) = \Pochhammersym{a}{n}\KummerconfhyperU@{n+a}{b}{z}} | w*(n)= pochhammer(a, n)*KummerU(n + a, b, z) |
w*(n)= Pochhammer[a, n]*HypergeometricU[n + a, b, z] |
Failure | Failure | Fail 1.520419005+1.650199040*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}2.873866917+2.939587822*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}4.267041895+4.298527135*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}1.371726075+1.394092488*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}... skip entries to safe data |
Skip |
| 13.29.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-a} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a-b+1}{s}}{s!}w(s)} | (z)^(- a)= sum((pochhammer(a - b + 1, s))/(factorial(s))*w*(s), s = 0..infinity) |
(z)^(- a)= Sum[Divide[Pochhammer[a - b + 1, s],(s)!]*w*(s), {s, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 13.31.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{a}\KummerconfhyperU@{a}{1+a-b}{z} = \lim_{n\to\infty}\frac{A_{n}(z)}{B_{n}(z)}} | (z)^(a)* KummerU(a, 1 + a - b, z)= limit((A[n]*(z))/(B[n]*(z)), n = infinity) |
(z)^(a)* HypergeometricU[a, 1 + a - b, z]= Limit[Divide[Subscript[A, n]*(z),Subscript[B, n]*(z)], n -> Infinity] |
Failure | Failure | Skip | Skip |