Results of Hypergeometric Function

From DRMF
Revision as of 14:40, 19 January 2020 by Admin (talk | contribs) (Created page with "{| class="wikitable sortable" |- ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica |- | [...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
15.1.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{2}{1}@{a,b}{c}{z} = \hyperF@{a}{b}{c}{z}} hypergeom([a , b], [c], z)= hypergeom([a, b], [c], z) HypergeometricPFQ[{a , b}, {c}, z]= Hypergeometric2F1[a, b, c, z] Successful Successful - -
15.1.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{c}{z} = \hyperF@@{a}{b}{c}{z}} hypergeom([a, b], [c], z)= hypergeom([a, b], [c], z) Hypergeometric2F1[a, b, c, z]= Hypergeometric2F1[a, b, c, z] Successful Successful - -
15.1.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{c}{z}} (hypergeom([a, b], [c], z))/(GAMMA(c))= hypergeom([a, b], [c], z)/GAMMA(c) Divide[Hypergeometric2F1[a, b, c, z],Gamma[c]]= Hypergeometric2F1Regularized[a, b, c, z] Successful Successful - -
15.1.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{a}{b}{c}{z} = \hyperOlverF@@{a}{b}{c}{z}} hypergeom([a, b], [c], z)/GAMMA(c)= hypergeom([a, b], [c], z)/GAMMA(c) Hypergeometric2F1Regularized[a, b, c, z]= Hypergeometric2F1Regularized[a, b, c, z] Successful Successful - -
15.1.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{c}{z} = \genhyperOlverF{2}{1}@{a,b}{c}{z}} hypergeom([a, b], [c], z)/GAMMA(c)= hypergeom([a , b], [c], z) Hypergeometric2F1Regularized[a, b, c, z]= HypergeometricPFQRegularized[{a , b}, {c}, z] Failure Successful Skip -
15.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{c}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}\Pochhammersym{b}{s}}{\Pochhammersym{c}{s}s!}z^{s}} hypergeom([a, b], [c], z)= sum((pochhammer(a, s)*pochhammer(b, s))/(pochhammer(c, s)*factorial(s))*(z)^(s), s = 0..infinity) Hypergeometric2F1[a, b, c, z]= Sum[Divide[Pochhammer[a, s]*Pochhammer[b, s],Pochhammer[c, s]*(s)!]*(z)^(s), {s, 0, Infinity}] Failure Successful Skip -
15.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{a}{b}{c}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}\Pochhammersym{b}{s}}{\EulerGamma@{c+s}s!}z^{s}} hypergeom([a, b], [c], z)/GAMMA(c)= sum((pochhammer(a, s)*pochhammer(b, s))/(GAMMA(c + s)*factorial(s))*(z)^(s), s = 0..infinity) Hypergeometric2F1Regularized[a, b, c, z]= Sum[Divide[Pochhammer[a, s]*Pochhammer[b, s],Gamma[c + s]*(s)!]*(z)^(s), {s, 0, Infinity}] Successful Failure - Skip
15.2.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{c}{x+\iunit 0}-\hyperOlverF@@{a}{b}{c}{x-\iunit 0} = \frac{2\pi\iunit}{\EulerGamma@{a}\EulerGamma@{b}}(x-1)^{c-a-b}\hyperOlverF@@{c-a}{c-b}{c-a-b+1}{1-x}} hypergeom([a, b], [c], x + I*0)/GAMMA(c)- hypergeom([a, b], [c], x - I*0)/GAMMA(c)=(2*Pi*I)/(GAMMA(a)*GAMMA(b))*(x - 1)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - x)/GAMMA(c - a - b + 1) Hypergeometric2F1Regularized[a, b, c, x + I*0]- Hypergeometric2F1Regularized[a, b, c, x - I*0]=Divide[2*Pi*I,Gamma[a]*Gamma[b]]*(x - 1)^(c - a - b)* Hypergeometric2F1Regularized[c - a, c - b, c - a - b + 1, 1 - x] Failure Failure
Fail
-487.8169477+316.7970546*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), x = 3/2}
-50479.20446+110828.3499*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2), x = 3/2}
-163338913.7+140350694.8*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)-I*2^(1/2), x = 3/2}
45522.85325+151628.5675*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = -2^(1/2)+I*2^(1/2), x = 3/2}
... skip entries to safe data
Fail
Complex[-487.81694810081785, 316.7970557265091] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, Rational[3, 2]]}
Complex[-50479.2047214623, 110828.3501851795] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, Rational[3, 2]]}
Complex[-1.633389146290397*^8, 1.4035069565108505*^8] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, Rational[3, 2]]}
Complex[45522.853876442554, 151628.56778915678] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, Rational[3, 2]]}
... skip entries to safe data
15.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{c\to-n}\frac{\hyperF@{a}{b}{c}{z}}{\EulerGamma@{c}} = \hyperOlverF@{a}{b}{-n}{z}} limit((hypergeom([a, b], [c], z))/(GAMMA(c)), c = - n)= hypergeom([a, b], [- n], z)/GAMMA(- n) Limit[Divide[Hypergeometric2F1[a, b, c, z],Gamma[c]], c -> - n]= Hypergeometric2F1Regularized[a, b, - n, z] Successful Successful - -
15.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{a}{b}{-n}{z} = \frac{\Pochhammersym{a}{n+1}\Pochhammersym{b}{n+1}}{(n+1)!}z^{n+1}\hyperF@{a+n+1}{b+n+1}{n+2}{z}} hypergeom([a, b], [- n], z)/GAMMA(- n)=(pochhammer(a, n + 1)*pochhammer(b, n + 1))/(factorial(n + 1))*(z)^(n + 1)* hypergeom([a + n + 1, b + n + 1], [n + 2], z) Hypergeometric2F1Regularized[a, b, - n, z]=Divide[Pochhammer[a, n + 1]*Pochhammer[b, n + 1],(n + 1)!]*(z)^(n + 1)* Hypergeometric2F1[a + n + 1, b + n + 1, n + 2, z] Failure Failure
Fail
Float(undefined)+Float(undefined)*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}
Float(undefined)+Float(undefined)*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}
Float(undefined)+Float(undefined)*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}
Float(undefined)+Float(undefined)*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
15.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{-m}{b}{c}{z} = \sum_{n=0}^{m}\frac{\Pochhammersym{-m}{n}\Pochhammersym{b}{n}}{\Pochhammersym{c}{n}{n!}}z^{n}} hypergeom([- m, b], [c], z)= sum((pochhammer(- m, n)*pochhammer(b, n))/(pochhammer(c, n)*factorial(n))*(z)^(n), n = 0..m) Hypergeometric2F1[- m, b, c, z]= Sum[Divide[Pochhammer[- m, n]*Pochhammer[b, n],Pochhammer[c, n]*(n)!]*(z)^(n), {n, 0, m}] Successful Successful - -
15.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{m}\frac{\Pochhammersym{-m}{n}\Pochhammersym{b}{n}}{\Pochhammersym{c}{n}{n!}}z^{n} = \sum_{n=0}^{m}(-1)^{n}\binom{m}{n}\frac{\Pochhammersym{b}{n}}{\Pochhammersym{c}{n}}z^{n}} sum((pochhammer(- m, n)*pochhammer(b, n))/(pochhammer(c, n)*factorial(n))*(z)^(n), n = 0..m)= sum((- 1)^(n)*binomial(m,n)*(pochhammer(b, n))/(pochhammer(c, n))*(z)^(n), n = 0..m) Sum[Divide[Pochhammer[- m, n]*Pochhammer[b, n],Pochhammer[c, n]*(n)!]*(z)^(n), {n, 0, m}]= Sum[(- 1)^(n)*Binomial[m,n]*Divide[Pochhammer[b, n],Pochhammer[c, n]]*(z)^(n), {n, 0, m}] Successful Successful - -
15.2.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{-m}{b}{-m-\ell}{z} = \lim_{c\to-m-\ell}\left(\lim_{a\to-m}\hyperF@@{a}{b}{c}{z}\right)} hypergeom([- m, b], [- m - ell], z)= limit(limit(hypergeom([a, b], [c], z), a = - m), c = - m - ell) Hypergeometric2F1[- m, b, - m - \[ScriptL], z]= Limit[Limit[Hypergeometric2F1[a, b, c, z], a -> - m], c -> - m - \[ScriptL]] Failure Successful Skip -
15.2.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{-m}{b}{-m-\ell}{z} = \lim_{a\to-m}\hyperF@@{a}{b}{a-\ell}{z}} hypergeom([- m, b], [- m - ell], z)= limit(hypergeom([a, b], [a - ell], z), a = - m) Hypergeometric2F1[- m, b, - m - \[ScriptL], z]= Limit[Hypergeometric2F1[a, b, a - \[ScriptL], z], a -> - m] Successful Successful - -
15.4.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{1}{1}{2}{z} = -z^{-1}\ln@{1-z}} hypergeom([1, 1], [2], z)= - (z)^(- 1)* ln(1 - z) Hypergeometric2F1[1, 1, 2, z]= - (z)^(- 1)* Log[1 - z] Successful Successful - -
15.4.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\tfrac{1}{2}}{1}{\tfrac{3}{2}}{z^{2}} = \frac{1}{2z}\ln@{\frac{1+z}{1-z}}} hypergeom([(1)/(2), 1], [(3)/(2)], (z)^(2))=(1)/(2*z)*ln((1 + z)/(1 - z)) Hypergeometric2F1[Divide[1,2], 1, Divide[3,2], (z)^(2)]=Divide[1,2*z]*Log[Divide[1 + z,1 - z]] Successful Failure - Successful
15.4.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\tfrac{1}{2}}{1}{\tfrac{3}{2}}{-z^{2}} = z^{-1}\atan@@{z}} hypergeom([(1)/(2), 1], [(3)/(2)], - (z)^(2))= (z)^(- 1)* arctan(z) Hypergeometric2F1[Divide[1,2], 1, Divide[3,2], - (z)^(2)]= (z)^(- 1)* ArcTan[z] Failure Successful Successful -
15.4.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\tfrac{1}{2}}{\tfrac{1}{2}}{\tfrac{3}{2}}{z^{2}} = z^{-1}\asin@@{z}} hypergeom([(1)/(2), (1)/(2)], [(3)/(2)], (z)^(2))= (z)^(- 1)* arcsin(z) Hypergeometric2F1[Divide[1,2], Divide[1,2], Divide[3,2], (z)^(2)]= (z)^(- 1)* ArcSin[z] Successful Successful - -
15.4.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\tfrac{1}{2}}{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = z^{-1}\ln@{z+\sqrt{1+z^{2}}}} hypergeom([(1)/(2), (1)/(2)], [(3)/(2)], - (z)^(2))= (z)^(- 1)* ln(z +sqrt(1 + (z)^(2))) Hypergeometric2F1[Divide[1,2], Divide[1,2], Divide[3,2], - (z)^(2)]= (z)^(- 1)* Log[z +Sqrt[1 + (z)^(2)]] Failure Successful Successful -
15.4#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{a}{z} = (1-z)^{-b}} hypergeom([a, b], [a], z)=(1 - z)^(- b) Hypergeometric2F1[a, b, a, z]=(1 - z)^(- b) Successful Successful - -
15.4#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{b}{z} = (1-z)^{-a}} hypergeom([a, b], [b], z)=(1 - z)^(- a) Hypergeometric2F1[a, b, b, z]=(1 - z)^(- a) Successful Successful - -
15.4.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{1}{2}}{z^{2}} = \tfrac{1}{2}\left((1+z)^{-2a}+(1-z)^{-2a}\right)} hypergeom([a, (1)/(2)+ a], [(1)/(2)], (z)^(2))=(1)/(2)*((1 + z)^(- 2*a)+(1 - z)^(- 2*a)) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[1,2], (z)^(2)]=Divide[1,2]*((1 + z)^(- 2*a)+(1 - z)^(- 2*a)) Successful Successful - -
15.4.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{1}{2}}{-\tan^{2}@@{z}} = (\cos@@{z})^{2a}\cos@{2az}} hypergeom([a, (1)/(2)+ a], [(1)/(2)], - (tan(z))^(2))=(cos(z))^(2*a)* cos(2*a*z) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[1,2], - (Tan[z])^(2)]=(Cos[z])^(2*a)* Cos[2*a*z] Failure Failure
Fail
.62e-2-.88e-2*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
.62e-2-.88e-2*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.62e-2+.88e-2*I <- {a = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.62e-2+.88e-2*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
 Successful
15.4.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{3}{2}}{z^{2}} = \frac{1}{(2-4a)z}\left((1+z)^{1-2a}-(1-z)^{1-2a}\right)} hypergeom([a, (1)/(2)+ a], [(3)/(2)], (z)^(2))=(1)/((2 - 4*a)* z)*((1 + z)^(1 - 2*a)-(1 - z)^(1 - 2*a)) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[3,2], (z)^(2)]=Divide[1,(2 - 4*a)* z]*((1 + z)^(1 - 2*a)-(1 - z)^(1 - 2*a)) Successful Successful - -
15.4.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{3}{2}}{-\tan^{2}@@{z}} = (\cos@@{z})^{2a}\frac{\sin@{(1-2a)z}}{(1-2a)\sin@@{z}}} hypergeom([a, (1)/(2)+ a], [(3)/(2)], - (tan(z))^(2))=(cos(z))^(2*a)*(sin((1 - 2*a)* z))/((1 - 2*a)* sin(z)) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[3,2], - (Tan[z])^(2)]=(Cos[z])^(2*a)*Divide[Sin[(1 - 2*a)* z],(1 - 2*a)* Sin[z]] Failure Failure Successful Successful
15.4.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{-a}{a}{\tfrac{1}{2}}{-z^{2}} = \tfrac{1}{2}\left(\left(\sqrt{1+z^{2}}+z\right)^{2a}+\left(\sqrt{1+z^{2}}-z\right)^{2a}\right)} hypergeom([- a, a], [(1)/(2)], - (z)^(2))=(1)/(2)*((sqrt(1 + (z)^(2))+ z)^(2*a)+(sqrt(1 + (z)^(2))- z)^(2*a)) Hypergeometric2F1[- a, a, Divide[1,2], - (z)^(2)]=Divide[1,2]*((Sqrt[1 + (z)^(2)]+ z)^(2*a)+(Sqrt[1 + (z)^(2)]- z)^(2*a)) Failure Failure Successful Successful
15.4.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{-a}{a}{\tfrac{1}{2}}{\sin^{2}@@{z}} = \cos@{2az}} hypergeom([- a, a], [(1)/(2)], (sin(z))^(2))= cos(2*a*z) Hypergeometric2F1[- a, a, Divide[1,2], (Sin[z])^(2)]= Cos[2*a*z] Failure Failure Successful Successful
15.4.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{1-a}{\tfrac{1}{2}}{-z^{2}} = \frac{1}{2\sqrt{1+z^{2}}}\left(\left(\sqrt{1+z^{2}}+z\right)^{2a-1}+\left(\sqrt{1+z^{2}}-z\right)^{2a-1}\right)} hypergeom([a, 1 - a], [(1)/(2)], - (z)^(2))=(1)/(2*sqrt(1 + (z)^(2)))*((sqrt(1 + (z)^(2))+ z)^(2*a - 1)+(sqrt(1 + (z)^(2))- z)^(2*a - 1)) Hypergeometric2F1[a, 1 - a, Divide[1,2], - (z)^(2)]=Divide[1,2*Sqrt[1 + (z)^(2)]]*((Sqrt[1 + (z)^(2)]+ z)^(2*a - 1)+(Sqrt[1 + (z)^(2)]- z)^(2*a - 1)) Successful Failure - Successful
15.4.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{1-a}{\tfrac{1}{2}}{\sin^{2}@@{z}} = \frac{\cos@{(2a-1)z}}{\cos@@{z}}} hypergeom([a, 1 - a], [(1)/(2)], (sin(z))^(2))=(cos((2*a - 1)* z))/(cos(z)) Hypergeometric2F1[a, 1 - a, Divide[1,2], (Sin[z])^(2)]=Divide[Cos[(2*a - 1)* z],Cos[z]] Failure Failure Successful Successful
15.4.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{1-a}{\tfrac{3}{2}}{-z^{2}} = \frac{1}{(2-4a)z}\left(\left(\sqrt{1+z^{2}}+z\right)^{1-2a}-\left(\sqrt{1+z^{2}}-z\right)^{1-2a}\right)} hypergeom([a, 1 - a], [(3)/(2)], - (z)^(2))=(1)/((2 - 4*a)* z)*((sqrt(1 + (z)^(2))+ z)^(1 - 2*a)-(sqrt(1 + (z)^(2))- z)^(1 - 2*a)) Hypergeometric2F1[a, 1 - a, Divide[3,2], - (z)^(2)]=Divide[1,(2 - 4*a)* z]*((Sqrt[1 + (z)^(2)]+ z)^(1 - 2*a)-(Sqrt[1 + (z)^(2)]- z)^(1 - 2*a)) Failure Failure Successful Successful
15.4.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{1-a}{\tfrac{3}{2}}{\sin^{2}@@{z}} = \frac{\sin@{(2a-1)z}}{(2a-1)\sin@@{z}}} hypergeom([a, 1 - a], [(3)/(2)], (sin(z))^(2))=(sin((2*a - 1)* z))/((2*a - 1)* sin(z)) Hypergeometric2F1[a, 1 - a, Divide[3,2], (Sin[z])^(2)]=Divide[Sin[(2*a - 1)* z],(2*a - 1)* Sin[z]] Successful Failure - Successful
15.4.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{1+2a}{z} = \left(\tfrac{1}{2}+\tfrac{1}{2}\sqrt{1-z}\right)^{-2a}} hypergeom([a, (1)/(2)+ a], [1 + 2*a], z)=((1)/(2)+(1)/(2)*sqrt(1 - z))^(- 2*a) Hypergeometric2F1[a, Divide[1,2]+ a, 1 + 2*a, z]=(Divide[1,2]+Divide[1,2]*Sqrt[1 - z])^(- 2*a) Failure Successful Successful -
15.4.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{2a}{z} = \frac{1}{\sqrt{1-z}}\left(\tfrac{1}{2}+\tfrac{1}{2}\sqrt{1-z}\right)^{1-2a}} hypergeom([a, (1)/(2)+ a], [2*a], z)=(1)/(sqrt(1 - z))*((1)/(2)+(1)/(2)*sqrt(1 - z))^(1 - 2*a) Hypergeometric2F1[a, Divide[1,2]+ a, 2*a, z]=Divide[1,Sqrt[1 - z]]*(Divide[1,2]+Divide[1,2]*Sqrt[1 - z])^(1 - 2*a) Failure Successful Successful -
15.4.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a+1}{b}{a}{z} = \left(1-(1-(\ifrac{b}{a}))z\right)(1-z)^{-1-b}} hypergeom([a + 1, b], [a], z)=(1 -(1 -((b)/(a)))*z)*(1 - z)^(- 1 - b) Hypergeometric2F1[a + 1, b, a, z]=(1 -(1 -(Divide[b,a]))*z)*(1 - z)^(- 1 - b) Successful Successful - -
15.4.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{c}{1} = \frac{\EulerGamma@{c}\EulerGamma@{c-a-b}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}} hypergeom([a, b], [c], 1)=(GAMMA(c)*GAMMA(c - a - b))/(GAMMA(c - a)*GAMMA(c - b)) Hypergeometric2F1[a, b, c, 1]=Divide[Gamma[c]*Gamma[c - a - b],Gamma[c - a]*Gamma[c - b]] Successful Failure -
Fail
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
15.4.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 1-}\frac{\hyperF@{a}{b}{a+b}{z}}{-\ln@{1-z}} = \frac{\EulerGamma@{a+b}}{\EulerGamma@{a}\EulerGamma@{b}}} limit((hypergeom([a, b], [a + b], z))/(- ln(1 - z)), z = 1, left)=(GAMMA(a + b))/(GAMMA(a)*GAMMA(b)) Limit[Divide[Hypergeometric2F1[a, b, a + b, z],- Log[1 - z]], z -> 1, Direction -> "FromBelow"]=Divide[Gamma[a + b],Gamma[a]*Gamma[b]] Successful Successful - -
15.4.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 1-}(1-z)^{a+b-c}\left(\hyperF@{a}{b}{c}{z}-\frac{\EulerGamma@{c}\EulerGamma@{c-a-b}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}\right) = \frac{\EulerGamma@{c}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{b}}} limit((1 - z)^(a + b - c)*(hypergeom([a, b], [c], z)-(GAMMA(c)*GAMMA(c - a - b))/(GAMMA(c - a)*GAMMA(c - b))), z = 1, left)=(GAMMA(c)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(b)) Limit[(1 - z)^(a + b - c)*(Hypergeometric2F1[a, b, c, z]-Divide[Gamma[c]*Gamma[c - a - b],Gamma[c - a]*Gamma[c - b]]), z -> 1, Direction -> "FromBelow"]=Divide[Gamma[c]*Gamma[a + b - c],Gamma[a]*Gamma[b]] Failure Failure Skip Skip
15.4.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{z\to 1-}\frac{\hyperF@{a}{b}{c}{z}}{(1-z)^{c-a-b}} = \frac{\EulerGamma@{c}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{b}}} limit((hypergeom([a, b], [c], z))/((1 - z)^(c - a - b)), z = 1, left)=(GAMMA(c)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(b)) Limit[Divide[Hypergeometric2F1[a, b, c, z],(1 - z)^(c - a - b)], z -> 1, Direction -> "FromBelow"]=Divide[Gamma[c]*Gamma[a + b - c],Gamma[a]*Gamma[b]] Failure Failure Skip
Fail
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
DirectedInfinity[] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[c, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
15.4.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{-n}{b}{c}{1} = \frac{\Pochhammersym{c-b}{n}}{\Pochhammersym{c}{n}}} hypergeom([- n, b], [c], 1)=(pochhammer(c - b, n))/(pochhammer(c, n)) Hypergeometric2F1[- n, b, c, 1]=Divide[Pochhammer[c - b, n],Pochhammer[c, n]] Successful Failure - Successful
15.4.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\EulerGamma@{a+n}\EulerGamma@{b+n}}{\EulerGamma@{c+n}\EulerGamma@{d+n}} = \frac{\pi^{2}}{\sin@{\pi a}\sin@{\pi b}}\*\frac{\EulerGamma@{c+d-a-b-1}}{\EulerGamma@{c-a}\EulerGamma@{d-a}\EulerGamma@{c-b}\EulerGamma@{d-b}}} sum((GAMMA(a + n)*GAMMA(b + n))/(GAMMA(c + n)*GAMMA(d + n)), n = - infinity..infinity)=((Pi)^(2))/(sin(Pi*a)*sin(Pi*b))*(GAMMA(c + d - a - b - 1))/(GAMMA(c - a)*GAMMA(d - a)*GAMMA(c - b)*GAMMA(d - b)) Sum[Divide[Gamma[a + n]*Gamma[b + n],Gamma[c + n]*Gamma[d + n]], {n, - Infinity, Infinity}]=Divide[(Pi)^(2),Sin[Pi*a]*Sin[Pi*b]]*Divide[Gamma[c + d - a - b - 1],Gamma[c - a]*Gamma[d - a]*Gamma[c - b]*Gamma[d - b]] Failure Failure Skip Error
15.4.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{a-b+1}{-1} = \frac{\EulerGamma@{a-b+1}\EulerGamma@{\tfrac{1}{2}a+1}}{\EulerGamma@{a+1}\EulerGamma@{\tfrac{1}{2}a-b+1}}} hypergeom([a, b], [a - b + 1], - 1)=(GAMMA(a - b + 1)*GAMMA((1)/(2)*a + 1))/(GAMMA(a + 1)*GAMMA((1)/(2)*a - b + 1)) Hypergeometric2F1[a, b, a - b + 1, - 1]=Divide[Gamma[a - b + 1]*Gamma[Divide[1,2]*a + 1],Gamma[a + 1]*Gamma[Divide[1,2]*a - b + 1]] Successful Successful - -
15.4.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{1}{a}{a+1}{-1} = \tfrac{1}{2}a\left(\digamma@{\tfrac{1}{2}a+\tfrac{1}{2}}-\digamma@{\tfrac{1}{2}a}\right)} hypergeom([1, a], [a + 1], - 1)=(1)/(2)*a*(Psi((1)/(2)*a +(1)/(2))- Psi((1)/(2)*a)) Hypergeometric2F1[1, a, a + 1, - 1]=Divide[1,2]*a*(PolyGamma[Divide[1,2]*a +Divide[1,2]]- PolyGamma[Divide[1,2]*a]) Successful Successful - -
15.4.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{2}}{\tfrac{1}{2}} = \sqrt{\pi}\frac{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}b+\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}b+\tfrac{1}{2}}}} hypergeom([a, b], [(1)/(2)*a +(1)/(2)*b +(1)/(2)], (1)/(2))=sqrt(Pi)*(GAMMA((1)/(2)*a +(1)/(2)*b +(1)/(2)))/(GAMMA((1)/(2)*a +(1)/(2))*GAMMA((1)/(2)*b +(1)/(2))) Hypergeometric2F1[a, b, Divide[1,2]*a +Divide[1,2]*b +Divide[1,2], Divide[1,2]]=Sqrt[Pi]*Divide[Gamma[Divide[1,2]*a +Divide[1,2]*b +Divide[1,2]],Gamma[Divide[1,2]*a +Divide[1,2]]*Gamma[Divide[1,2]*b +Divide[1,2]]] Successful Successful - -
15.4.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{b}{\tfrac{1}{2}a+\tfrac{1}{2}b+1}{\tfrac{1}{2}} = \frac{2\sqrt{\pi}}{a-b}\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}b+1}\*\left(\frac{1}{\EulerGamma@{\tfrac{1}{2}a}\EulerGamma@{\tfrac{1}{2}b+\tfrac{1}{2}}}-\frac{1}{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}b}}\right)} hypergeom([a, b], [(1)/(2)*a +(1)/(2)*b + 1], (1)/(2))=(2*sqrt(Pi))/(a - b)*GAMMA((1)/(2)*a +(1)/(2)*b + 1)*((1)/(GAMMA((1)/(2)*a)*GAMMA((1)/(2)*b +(1)/(2)))-(1)/(GAMMA((1)/(2)*a +(1)/(2))*GAMMA((1)/(2)*b))) Hypergeometric2F1[a, b, Divide[1,2]*a +Divide[1,2]*b + 1, Divide[1,2]]=Divide[2*Sqrt[Pi],a - b]*Gamma[Divide[1,2]*a +Divide[1,2]*b + 1]*(Divide[1,Gamma[Divide[1,2]*a]*Gamma[Divide[1,2]*b +Divide[1,2]]]-Divide[1,Gamma[Divide[1,2]*a +Divide[1,2]]*Gamma[Divide[1,2]*b]]) Failure Failure
Fail
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2)}
Float(undefined)+Float(undefined)*I <- {a = 2^(1/2)-I*2^(1/2), b = 2^(1/2)-I*2^(1/2)}
Float(undefined)+Float(undefined)*I <- {a = -2^(1/2)-I*2^(1/2), b = -2^(1/2)-I*2^(1/2)}
Float(undefined)+Float(undefined)*I <- {a = -2^(1/2)+I*2^(1/2), b = -2^(1/2)+I*2^(1/2)}
 Successful
15.4.E30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{1-a}{b}{\tfrac{1}{2}} = \frac{2^{1-b}\sqrt{\pi}\EulerGamma@{b}}{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}b}\EulerGamma@{\tfrac{1}{2}b-\tfrac{1}{2}a+\tfrac{1}{2}}}} hypergeom([a, 1 - a], [b], (1)/(2))=((2)^(1 - b)*sqrt(Pi)*GAMMA(b))/(GAMMA((1)/(2)*a +(1)/(2)*b)*GAMMA((1)/(2)*b -(1)/(2)*a +(1)/(2))) Hypergeometric2F1[a, 1 - a, b, Divide[1,2]]=Divide[(2)^(1 - b)*Sqrt[Pi]*Gamma[b],Gamma[Divide[1,2]*a +Divide[1,2]*b]*Gamma[Divide[1,2]*b -Divide[1,2]*a +Divide[1,2]]] Successful Failure - Successful
15.4.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{3}{2}-2a}{-\tfrac{1}{3}} = \left(\frac{8}{9}\right)^{-2a}\frac{\EulerGamma@{\tfrac{4}{3}}\EulerGamma@{\tfrac{3}{2}-2a}}{\EulerGamma@{\tfrac{3}{2}}\EulerGamma@{\tfrac{4}{3}-2a}}} hypergeom([a, (1)/(2)+ a], [(3)/(2)- 2*a], -(1)/(3))=((8)/(9))^(- 2*a)*(GAMMA((4)/(3))*GAMMA((3)/(2)- 2*a))/(GAMMA((3)/(2))*GAMMA((4)/(3)- 2*a)) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[3,2]- 2*a, -Divide[1,3]]=(Divide[8,9])^(- 2*a)*Divide[Gamma[Divide[4,3]]*Gamma[Divide[3,2]- 2*a],Gamma[Divide[3,2]]*Gamma[Divide[4,3]- 2*a]] Failure Failure Successful Successful
15.4.E32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{a}{\tfrac{1}{2}+a}{\tfrac{5}{6}+\tfrac{2}{3}a}{\tfrac{1}{9}} = \sqrt{\pi}\left(\frac{3}{4}\right)^{a}\frac{\EulerGamma@{\tfrac{5}{6}+\tfrac{2}{3}a}}{\EulerGamma@{\tfrac{1}{2}+\tfrac{1}{3}a}\EulerGamma@{\tfrac{5}{6}+\tfrac{1}{3}a}}} hypergeom([a, (1)/(2)+ a], [(5)/(6)+(2)/(3)*a], (1)/(9))=sqrt(Pi)*((3)/(4))^(a)*(GAMMA((5)/(6)+(2)/(3)*a))/(GAMMA((1)/(2)+(1)/(3)*a)*GAMMA((5)/(6)+(1)/(3)*a)) Hypergeometric2F1[a, Divide[1,2]+ a, Divide[5,6]+Divide[2,3]*a, Divide[1,9]]=Sqrt[Pi]*(Divide[3,4])^(a)*Divide[Gamma[Divide[5,6]+Divide[2,3]*a],Gamma[Divide[1,2]+Divide[1,3]*a]*Gamma[Divide[5,6]+Divide[1,3]*a]] Failure Failure Successful Successful
15.4.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{3a}{\tfrac{1}{3}+a}{\tfrac{2}{3}+2a}{e^{\ifrac{\iunit\pi}{3}}} = \sqrt{\pi}e^{\ifrac{\iunit\pi a}{2}}\left(\frac{16}{27}\right)^{(3a+1)/6}\frac{\EulerGamma@{\frac{5}{6}+a}}{\EulerGamma@{\frac{2}{3}+a}\EulerGamma@{\frac{2}{3}}}} hypergeom([3*a, (1)/(3)+ a], [(2)/(3)+ 2*a], exp((I*Pi)/(3)))=sqrt(Pi)*exp((I*Pi*a)/(2))*((16)/(27))^((3*a + 1)/ 6)*(GAMMA((5)/(6)+ a))/(GAMMA((2)/(3)+ a)*GAMMA((2)/(3))) Hypergeometric2F1[3*a, Divide[1,3]+ a, Divide[2,3]+ 2*a, Exp[Divide[I*Pi,3]]]=Sqrt[Pi]*Exp[Divide[I*Pi*a,2]]*(Divide[16,27])^((3*a + 1)/ 6)*Divide[Gamma[Divide[5,6]+ a],Gamma[Divide[2,3]+ a]*Gamma[Divide[2,3]]] Failure Failure Successful Successful
15.5.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\hyperF@{a}{b}{c}{z} = \frac{ab}{c}\hyperF@{a+1}{b+1}{c+1}{z}} diff(hypergeom([a, b], [c], z), z)=(a*b)/(c)*hypergeom([a + 1, b + 1], [c + 1], z) D[Hypergeometric2F1[a, b, c, z], z]=Divide[a*b,c]*Hypergeometric2F1[a + 1, b + 1, c + 1, z] Successful Successful - -
15.5.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\hyperF@{a}{b}{c}{z} = \frac{\Pochhammersym{a}{n}\Pochhammersym{b}{n}}{\Pochhammersym{c}{n}}\*\hyperF@{a+n}{b+n}{c+n}{z}} diff(hypergeom([a, b], [c], z), [z$(n)])=(pochhammer(a, n)*pochhammer(b, n))/(pochhammer(c, n))* hypergeom([a + n, b + n], [c + n], z) D[Hypergeometric2F1[a, b, c, z], {z, n}]=Divide[Pochhammer[a, n]*Pochhammer[b, n],Pochhammer[c, n]]* Hypergeometric2F1[a + n, b + n, c + n, z] Successful Successful - -
15.5.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(z\deriv{}{z}z\right)^{n}\left(z^{a-1}\hyperF@{a}{b}{c}{z}\right) = \Pochhammersym{a}{n}z^{a+n-1}\hyperF@{a+n}{b}{c}{z}} (z*diff(z, z))^(n)*((z)^(a - 1)* hypergeom([a, b], [c], z))= pochhammer(a, n)*(z)^(a + n - 1)* hypergeom([a + n, b], [c], z) (z*D[z, z])^(n)*((z)^(a - 1)* Hypergeometric2F1[a, b, c, z])= Pochhammer[a, n]*(z)^(a + n - 1)* Hypergeometric2F1[a + n, b, c, z] Failure Failure
Fail
-.6225095031e-1-.5644186814e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
.1785845766+.2832629970e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-.7314115943-.4867699196*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-34.57094218-72.21034026*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
 Skip
15.5.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{c-1}\hyperF@{a}{b}{c}{z}\right) = \Pochhammersym{c-n}{n}z^{c-n-1}\hyperF@{a}{b}{c-n}{z}} diff((z)^(c - 1)* hypergeom([a, b], [c], z), [z$(n)])= pochhammer(c - n, n)*(z)^(c - n - 1)* hypergeom([a, b], [c - n], z) D[(z)^(c - 1)* Hypergeometric2F1[a, b, c, z], {z, n}]= Pochhammer[c - n, n]*(z)^(c - n - 1)* Hypergeometric2F1[a, b, c - n, z] Failure Failure Skip Skip
15.5.E5 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^{c-a-1}(1-z)^{a+b-c}\hyperF@{a}{b}{c}{z}\right) = \Pochhammersym{c-a}{n}z^{c-a+n-1}(1-z)^{a-n+b-c}\*\hyperF@{a-n}{b}{c}{z}} (z*diff(z, z))^(n)*((z)^(c - a - 1)*(1 - z)^(a + b - c)* hypergeom([a, b], [c], z))= pochhammer(c - a, n)*(z)^(c - a + n - 1)*(1 - z)^(a - n + b - c)* hypergeom([a - n, b], [c], z) (z*D[z, z])^(n)*((z)^(c - a - 1)*(1 - z)^(a + b - c)* Hypergeometric2F1[a, b, c, z])= Pochhammer[c - a, n]*(z)^(c - a + n - 1)*(1 - z)^(a - n + b - c)* Hypergeometric2F1[a - n, b, c, z] Failure Failure
Fail
1.000000000-.2828427124e-9*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 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), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
.1131370849e-8+3.999999998*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 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), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
 Skip
15.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left((1-z)^{a+b-c}\hyperF@{a}{b}{c}{z}\right) = \frac{\Pochhammersym{c-a}{n}\Pochhammersym{c-b}{n}}{\Pochhammersym{c}{n}}(1-z)^{a+b-c-n}\*\hyperF@{a}{b}{c+n}{z}} diff((1 - z)^(a + b - c)* hypergeom([a, b], [c], z), [z$(n)])=(pochhammer(c - a, n)*pochhammer(c - b, n))/(pochhammer(c, n))*(1 - z)^(a + b - c - n)* hypergeom([a, b], [c + n], z) D[(1 - z)^(a + b - c)* Hypergeometric2F1[a, b, c, z], {z, n}]=Divide[Pochhammer[c - a, n]*Pochhammer[c - b, n],Pochhammer[c, n]]*(1 - z)^(a + b - c - n)* Hypergeometric2F1[a, b, c + n, z] Failure Failure Skip Skip
15.5.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left((1-z)\deriv{}{z}(1-z)\right)^{n}\left((1-z)^{a-1}\hyperF@{a}{b}{c}{z}\right) = (-1)^{n}\frac{\Pochhammersym{a}{n}\Pochhammersym{c-b}{n}}{\Pochhammersym{c}{n}}(1-z)^{a+n-1}\*\hyperF@{a+n}{b}{c+n}{z}} ((1 - z)*diff(1 - z, z))^(n)*((1 - z)^(a - 1)* hypergeom([a, b], [c], z))=(- 1)^(n)*(pochhammer(a, n)*pochhammer(c - b, n))/(pochhammer(c, n))*(1 - z)^(a + n - 1)* hypergeom([a + n, b], [c + n], z) ((1 - z)*D[1 - z, z])^(n)*((1 - z)^(a - 1)* Hypergeometric2F1[a, b, c, z])=(- 1)^(n)*Divide[Pochhammer[a, n]*Pochhammer[c - b, n],Pochhammer[c, n]]*(1 - z)^(a + n - 1)* Hypergeometric2F1[a + n, b, c + n, z] Failure Failure
Fail
-1.000000000+.574091994e-10*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-.4142135623-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
1.828427125-1.171572874*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-1.000000000+.254335130e-10*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
 Skip
15.5.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left((1-z)\deriv{}{z}(1-z)\right)^{n}\left(z^{c-1}(1-z)^{b-c}\hyperF@{a}{b}{c}{z}\right) = \Pochhammersym{c-n}{n}z^{c-n-1}(1-z)^{b-c+n}\*\hyperF@{a-n}{b}{c-n}{z}} ((1 - z)*diff(1 - z, z))^(n)*((z)^(c - 1)*(1 - z)^(b - c)* hypergeom([a, b], [c], z))= pochhammer(c - n, n)*(z)^(c - n - 1)*(1 - z)^(b - c + n)* hypergeom([a - n, b], [c - n], z) ((1 - z)*D[1 - z, z])^(n)*((z)^(c - 1)*(1 - z)^(b - c)* Hypergeometric2F1[a, b, c, z])= Pochhammer[c - n, n]*(z)^(c - n - 1)*(1 - z)^(b - c + n)* Hypergeometric2F1[a - n, b, c - n, z] Failure Failure
Fail
.7567079467e-2-.4498677196e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
.3281146176e-1-.3488816280e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
.1860334783e-1+.1631943039e-1*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-43.13343073-5.34730687*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
 Skip
15.5.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\left(z^{c-1}(1-z)^{a+b-c}\hyperF@{a}{b}{c}{z}\right) = \Pochhammersym{c-n}{n}z^{c-n-1}(1-z)^{a+b-c-n}\*\hyperF@{a-n}{b-n}{c-n}{z}} diff((z)^(c - 1)*(1 - z)^(a + b - c)* hypergeom([a, b], [c], z), [z$(n)])= pochhammer(c - n, n)*(z)^(c - n - 1)*(1 - z)^(a + b - c - n)* hypergeom([a - n, b - n], [c - n], z) D[(z)^(c - 1)*(1 - z)^(a + b - c)* Hypergeometric2F1[a, b, c, z], {z, n}]= Pochhammer[c - n, n]*(z)^(c - n - 1)*(1 - z)^(a + b - c - n)* Hypergeometric2F1[a - n, b - n, c - n, z] Failure Failure Skip Skip
15.5.E10 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]]]]}
15.5.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (c-a)\hyperF@{a-1}{b}{c}{z}+\left(2a-c+(b-a)z\right)\hyperF@{a}{b}{c}{z}+a(z-1)\hyperF@{a+1}{b}{c}{z} = 0} (c - a)* hypergeom([a - 1, b], [c], z)+(2*a - c +(b - a)*z)* hypergeom([a, b], [c], z)+ a*(z - 1)* hypergeom([a + 1, b], [c], z)= 0 (c - a)* Hypergeometric2F1[a - 1, b, c, z]+(2*a - c +(b - a)*z)* Hypergeometric2F1[a, b, c, z]+ a*(z - 1)* Hypergeometric2F1[a + 1, b, c, z]= 0 Successful Successful - -
15.5.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (b-a)\hyperF@{a}{b}{c}{z}+a\hyperF@{a+1}{b}{c}{z}-b\hyperF@{a}{b+1}{c}{z} = 0} (b - a)* hypergeom([a, b], [c], z)+ a*hypergeom([a + 1, b], [c], z)- b*hypergeom([a, b + 1], [c], z)= 0 (b - a)* Hypergeometric2F1[a, b, c, z]+ a*Hypergeometric2F1[a + 1, b, c, z]- b*Hypergeometric2F1[a, b + 1, c, z]= 0 Successful Successful - -
15.5.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (c-a-b)\hyperF@{a}{b}{c}{z}+a(1-z)\hyperF@{a+1}{b}{c}{z}-(c-b)\hyperF@{a}{b-1}{c}{z} = 0} (c - a - b)* hypergeom([a, b], [c], z)+ a*(1 - z)* hypergeom([a + 1, b], [c], z)-(c - b)* hypergeom([a, b - 1], [c], z)= 0 (c - a - b)* Hypergeometric2F1[a, b, c, z]+ a*(1 - z)* Hypergeometric2F1[a + 1, b, c, z]-(c - b)* Hypergeometric2F1[a, b - 1, c, z]= 0 Successful Successful - -
15.5.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c\left(a+(b-c)z\right)\hyperF@{a}{b}{c}{z}-ac(1-z)\hyperF@{a+1}{b}{c}{z}+(c-a)(c-b)z\hyperF@{a}{b}{c+1}{z} = 0} c*(a +(b - c)*z)* hypergeom([a, b], [c], z)- a*c*(1 - z)* hypergeom([a + 1, b], [c], z)+(c - a)*(c - b)* z*hypergeom([a, b], [c + 1], z)= 0 c*(a +(b - c)*z)* Hypergeometric2F1[a, b, c, z]- a*c*(1 - z)* Hypergeometric2F1[a + 1, b, c, z]+(c - a)*(c - b)* z*Hypergeometric2F1[a, b, c + 1, z]= 0 Successful Successful - -
15.5.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (c-a-1)\hyperF@{a}{b}{c}{z}+a\hyperF@{a+1}{b}{c}{z}-(c-1)\hyperF@{a}{b}{c-1}{z} = 0} (c - a - 1)* hypergeom([a, b], [c], z)+ a*hypergeom([a + 1, b], [c], z)-(c - 1)* hypergeom([a, b], [c - 1], z)= 0 (c - a - 1)* Hypergeometric2F1[a, b, c, z]+ a*Hypergeometric2F1[a + 1, b, c, z]-(c - 1)* Hypergeometric2F1[a, b, c - 1, z]= 0 Successful Successful - -
15.5.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c(1-z)\hyperF@{a}{b}{c}{z}-c\hyperF@{a-1}{b}{c}{z}+(c-b)z\hyperF@{a}{b}{c+1}{z} = 0} c*(1 - z)* hypergeom([a, b], [c], z)- c*hypergeom([a - 1, b], [c], z)+(c - b)* z*hypergeom([a, b], [c + 1], z)= 0 c*(1 - z)* Hypergeometric2F1[a, b, c, z]- c*Hypergeometric2F1[a - 1, b, c, z]+(c - b)* z*Hypergeometric2F1[a, b, c + 1, z]= 0 Successful Successful - -
15.5.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(a-1+(b+1-c)z\right)\hyperF@{a}{b}{c}{z}+(c-a)\hyperF@{a-1}{b}{c}{z}-(c-1)(1-z)\hyperF@{a}{b}{c-1}{z} = 0} (a - 1 +(b + 1 - c)*z)* hypergeom([a, b], [c], z)+(c - a)* hypergeom([a - 1, b], [c], z)-(c - 1)*(1 - z)* hypergeom([a, b], [c - 1], z)= 0 (a - 1 +(b + 1 - c)*z)* Hypergeometric2F1[a, b, c, z]+(c - a)* Hypergeometric2F1[a - 1, b, c, z]-(c - 1)*(1 - z)* Hypergeometric2F1[a, b, c - 1, z]= 0 Successful Successful - -
15.5.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c(c-1)(z-1)\hyperF@{a}{b}{c-1}{z}+{c\left(c-1-(2c-a-b-1)z\right)}\hyperF@{a}{b}{c}{z}+(c-a)(c-b)z\hyperF@{a}{b}{c+1}{z} = 0} c*(c - 1)*(z - 1)* hypergeom([a, b], [c - 1], z)+c*(c - 1 -(2*c - a - b - 1)*z)*hypergeom([a, b], [c], z)+(c - a)*(c - b)* z*hypergeom([a, b], [c + 1], z)= 0 c*(c - 1)*(z - 1)* Hypergeometric2F1[a, b, c - 1, z]+c*(c - 1 -(2*c - a - b - 1)*z)*Hypergeometric2F1[a, b, c, z]+(c - a)*(c - b)* z*Hypergeometric2F1[a, b, c + 1, z]= 0 Successful Successful - -
15.5.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {z(1-z)(a+1)(b+1)}\hyperF@{a+2}{b+2}{c+2}{z}+{(c-(a+b+1)z)(c+1)}\hyperF@{a+1}{b+1}{c+1}{z}-{c(c+1)}\hyperF@{a}{b}{c}{z} = 0} z*(1 - z)*(a + 1)*(b + 1)*hypergeom([a + 2, b + 2], [c + 2], z)+(c -(a + b + 1)*z)*(c + 1)*hypergeom([a + 1, b + 1], [c + 1], z)-c*(c + 1)*hypergeom([a, b], [c], z)= 0 z*(1 - z)*(a + 1)*(b + 1)*Hypergeometric2F1[a + 2, b + 2, c + 2, z]+(c -(a + b + 1)*z)*(c + 1)*Hypergeometric2F1[a + 1, b + 1, c + 1, z]-c*(c + 1)*Hypergeometric2F1[a, b, c, z]= 0 Successful Successful - -
15.5.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)\left(\ideriv{\hyperF@{a}{b}{c}{z}}{z}\right) = (c-a)\hyperF@{a-1}{b}{c}{z}+(a-c+bz)\hyperF@{a}{b}{c}{z}} z*(1 - z)*(diff(hypergeom([a, b], [c], z), z))=(c - a)* hypergeom([a - 1, b], [c], z)+(a - c + b*z)* hypergeom([a, b], [c], z) z*(1 - z)*(D[Hypergeometric2F1[a, b, c, z], z])=(c - a)* Hypergeometric2F1[a - 1, b, c, z]+(a - c + b*z)* Hypergeometric2F1[a, b, c, z] Successful Successful - -
15.5.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (c-a)\hyperF@{a-1}{b}{c}{z}+(a-c+bz)\hyperF@{a}{b}{c}{z} = (c-b)\hyperF@{a}{b-1}{c}{z}+(b-c+az)\hyperF@{a}{b}{c}{z}} (c - a)* hypergeom([a - 1, b], [c], z)+(a - c + b*z)* hypergeom([a, b], [c], z)=(c - b)* hypergeom([a, b - 1], [c], z)+(b - c + a*z)* hypergeom([a, b], [c], z) (c - a)* Hypergeometric2F1[a - 1, b, c, z]+(a - c + b*z)* Hypergeometric2F1[a, b, c, z]=(c - b)* Hypergeometric2F1[a, b - 1, c, z]+(b - c + a*z)* Hypergeometric2F1[a, b, c, z] Successful Successful - -
15.5.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c(1-z)\left(\ideriv{\hyperF@{a}{b}{c}{z}}{z}\right) = (c-a)(c-b)\hyperF@{a}{b}{c+1}{z}+c(a+b-c)\hyperF@{a}{b}{c}{z}} c*(1 - z)*(diff(hypergeom([a, b], [c], z), z))=(c - a)*(c - b)* hypergeom([a, b], [c + 1], z)+ c*(a + b - c)* hypergeom([a, b], [c], z) c*(1 - z)*(D[Hypergeometric2F1[a, b, c, z], z])=(c - a)*(c - b)* Hypergeometric2F1[a, b, c + 1, z]+ c*(a + b - c)* Hypergeometric2F1[a, b, c, z] Successful Successful - -
15.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{c}{z} = (1-z)^{-a}\hyperOlverF@@{a}{c-b}{c}{\frac{z}{z-1}}} hypergeom([a, b], [c], z)/GAMMA(c)=(1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1))/GAMMA(c) Hypergeometric2F1Regularized[a, b, c, z]=(1 - z)^(- a)* Hypergeometric2F1Regularized[a, c - b, c, Divide[z,z - 1]] Failure Failure Skip Skip
15.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{-a}\hyperOlverF@@{a}{c-b}{c}{\frac{z}{z-1}} = (1-z)^{-b}\hyperOlverF@@{c-a}{b}{c}{\frac{z}{z-1}}} (1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1))/GAMMA(c)=(1 - z)^(- b)* hypergeom([c - a, b], [c], (z)/(z - 1))/GAMMA(c) (1 - z)^(- a)* Hypergeometric2F1Regularized[a, c - b, c, Divide[z,z - 1]]=(1 - z)^(- b)* Hypergeometric2F1Regularized[c - a, b, c, Divide[z,z - 1]] Failure Failure Skip Skip
15.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{-b}\hyperOlverF@@{c-a}{b}{c}{\frac{z}{z-1}} = (1-z)^{c-a-b}\hyperOlverF@@{c-a}{c-b}{c}{z}} (1 - z)^(- b)* hypergeom([c - a, b], [c], (z)/(z - 1))/GAMMA(c)=(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c], z)/GAMMA(c) (1 - z)^(- b)* Hypergeometric2F1Regularized[c - a, b, c, Divide[z,z - 1]]=(1 - z)^(c - a - b)* Hypergeometric2F1Regularized[c - a, c - b, c, z] Failure Failure Skip Skip
15.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi(b-a)}}{\pi}\hyperOlverF@@{a}{b}{c}{z} = \frac{(-z)^{-a}}{\EulerGamma@{b}\EulerGamma@{c-a}}\hyperOlverF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}-\frac{(-z)^{-b}}{\EulerGamma@{a}\EulerGamma@{c-b}}\hyperOlverF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}} (sin(Pi*(b - a)))/(Pi)*hypergeom([a, b], [c], z)/GAMMA(c)=((- z)^(- a))/(GAMMA(b)*GAMMA(c - a))*hypergeom([a, a - c + 1], [a - b + 1], (1)/(z))/GAMMA(a - b + 1)-((- z)^(- b))/(GAMMA(a)*GAMMA(c - b))*hypergeom([b, b - c + 1], [b - a + 1], (1)/(z))/GAMMA(b - a + 1) Divide[Sin[Pi*(b - a)],Pi]*Hypergeometric2F1Regularized[a, b, c, z]=Divide[(- z)^(- a),Gamma[b]*Gamma[c - a]]*Hypergeometric2F1Regularized[a, a - c + 1, a - b + 1, Divide[1,z]]-Divide[(- z)^(- b),Gamma[a]*Gamma[c - b]]*Hypergeometric2F1Regularized[b, b - c + 1, b - a + 1, Divide[1,z]] Failure Failure Skip Skip
15.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi(b-a)}}{\pi}\hyperOlverF@@{a}{b}{c}{z} = \frac{(1-z)^{-a}}{\EulerGamma@{b}\EulerGamma@{c-a}}\hyperOlverF@@{a}{c-b}{a-b+1}{\frac{1}{1-z}}-\frac{(1-z)^{-b}}{\EulerGamma@{a}\EulerGamma@{c-b}}\hyperOlverF@@{b}{c-a}{b-a+1}{\frac{1}{1-z}}} (sin(Pi*(b - a)))/(Pi)*hypergeom([a, b], [c], z)/GAMMA(c)=((1 - z)^(- a))/(GAMMA(b)*GAMMA(c - a))*hypergeom([a, c - b], [a - b + 1], (1)/(1 - z))/GAMMA(a - b + 1)-((1 - z)^(- b))/(GAMMA(a)*GAMMA(c - b))*hypergeom([b, c - a], [b - a + 1], (1)/(1 - z))/GAMMA(b - a + 1) Divide[Sin[Pi*(b - a)],Pi]*Hypergeometric2F1Regularized[a, b, c, z]=Divide[(1 - z)^(- a),Gamma[b]*Gamma[c - a]]*Hypergeometric2F1Regularized[a, c - b, a - b + 1, Divide[1,1 - z]]-Divide[(1 - z)^(- b),Gamma[a]*Gamma[c - b]]*Hypergeometric2F1Regularized[b, c - a, b - a + 1, Divide[1,1 - z]] Failure Failure Skip Skip
15.8.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi(c-a-b)}}{\pi}\hyperOlverF@@{a}{b}{c}{z} = \frac{1}{\EulerGamma@{c-a}\EulerGamma@{c-b}}\hyperOlverF@@{a}{b}{a+b-c+1}{1-z}-\frac{(1-z)^{c-a-b}}{\EulerGamma@{a}\EulerGamma@{b}}\hyperOlverF@@{c-a}{c-b}{c-a-b+1}{1-z}} (sin(Pi*(c - a - b)))/(Pi)*hypergeom([a, b], [c], z)/GAMMA(c)=(1)/(GAMMA(c - a)*GAMMA(c - b))*hypergeom([a, b], [a + b - c + 1], 1 - z)/GAMMA(a + b - c + 1)-((1 - z)^(c - a - b))/(GAMMA(a)*GAMMA(b))*hypergeom([c - a, c - b], [c - a - b + 1], 1 - z)/GAMMA(c - a - b + 1) Divide[Sin[Pi*(c - a - b)],Pi]*Hypergeometric2F1Regularized[a, b, c, z]=Divide[1,Gamma[c - a]*Gamma[c - b]]*Hypergeometric2F1Regularized[a, b, a + b - c + 1, 1 - z]-Divide[(1 - z)^(c - a - b),Gamma[a]*Gamma[b]]*Hypergeometric2F1Regularized[c - a, c - b, c - a - b + 1, 1 - z] Failure Failure Skip Skip
15.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi(c-a-b)}}{\pi}\hyperOlverF@@{a}{b}{c}{z} = \frac{z^{-a}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}\hyperOlverF@@{a}{a-c+1}{a+b-c+1}{1-\frac{1}{z}}-\frac{(1-z)^{c-a-b}z^{a-c}}{\EulerGamma@{a}\EulerGamma@{b}}\hyperOlverF@@{c-a}{1-a}{c-a-b+1}{1-\frac{1}{z}}} (sin(Pi*(c - a - b)))/(Pi)*hypergeom([a, b], [c], z)/GAMMA(c)=((z)^(- a))/(GAMMA(c - a)*GAMMA(c - b))*hypergeom([a, a - c + 1], [a + b - c + 1], 1 -(1)/(z))/GAMMA(a + b - c + 1)-((1 - z)^(c - a - b)* (z)^(a - c))/(GAMMA(a)*GAMMA(b))*hypergeom([c - a, 1 - a], [c - a - b + 1], 1 -(1)/(z))/GAMMA(c - a - b + 1) Divide[Sin[Pi*(c - a - b)],Pi]*Hypergeometric2F1Regularized[a, b, c, z]=Divide[(z)^(- a),Gamma[c - a]*Gamma[c - b]]*Hypergeometric2F1Regularized[a, a - c + 1, a + b - c + 1, 1 -Divide[1,z]]-Divide[(1 - z)^(c - a - b)* (z)^(a - c),Gamma[a]*Gamma[b]]*Hypergeometric2F1Regularized[c - a, 1 - a, c - a - b + 1, 1 -Divide[1,z]] Failure Failure Skip Skip
15.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{-m}{b}{c}{z} = \frac{(b)_{m}}{(c)_{m}}(-z)^{m}\hyperF@@{-m}{1-c-m}{1-b-m}{\frac{1}{z}}} hypergeom([- m, b], [c], z)=(b[m])/(c[m])*(- z)^(m)* hypergeom([- m, 1 - c - m], [1 - b - m], (1)/(z)) Hypergeometric2F1[- m, b, c, z]=Divide[Subscript[b, m],Subscript[c, m]]*(- z)^(m)* Hypergeometric2F1[- m, 1 - c - m, 1 - b - m, Divide[1,z]] Failure Failure Skip Skip
15.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(b)_{m}}{(c)_{m}}(-z)^{m}\hyperF@@{-m}{1-c-m}{1-b-m}{\frac{1}{z}} = \frac{(b)_{m}}{(c)_{m}}(1-z)^{m}\hyperF@@{-m}{c-b}{1-b-m}{\frac{1}{1-z}}} (b[m])/(c[m])*(- z)^(m)* hypergeom([- m, 1 - c - m], [1 - b - m], (1)/(z))=(b[m])/(c[m])*(1 - z)^(m)* hypergeom([- m, c - b], [1 - b - m], (1)/(1 - z)) Divide[Subscript[b, m],Subscript[c, m]]*(- z)^(m)* Hypergeometric2F1[- m, 1 - c - m, 1 - b - m, Divide[1,z]]=Divide[Subscript[b, m],Subscript[c, m]]*(1 - z)^(m)* Hypergeometric2F1[- m, c - b, 1 - b - m, Divide[1,1 - z]] Failure Failure Skip Skip
15.8.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{-m}{b}{c}{z} = \frac{(c-b)_{m}}{(c)_{m}}\hyperF@@{-m}{b}{b-c-m+1}{1-z}} hypergeom([- m, b], [c], z)=(c - b[m])/(c[m])*hypergeom([- m, b], [b - c - m + 1], 1 - z) Hypergeometric2F1[- m, b, c, z]=Divide[Subscript[c - b, m],Subscript[c, m]]*Hypergeometric2F1[- m, b, b - c - m + 1, 1 - z] Failure Failure Skip Skip
15.8.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(c-b)_{m}}{(c)_{m}}\hyperF@@{-m}{b}{b-c-m+1}{1-z} = \frac{(c-b)_{m}}{(c)_{m}}z^{m}\hyperF@@{-m}{1-c-m}{b-c-m+1}{1-\frac{1}{z}}} (c - b[m])/(c[m])*hypergeom([- m, b], [b - c - m + 1], 1 - z)=(c - b[m])/(c[m])*(z)^(m)* hypergeom([- m, 1 - c - m], [b - c - m + 1], 1 -(1)/(z)) Divide[Subscript[c - b, m],Subscript[c, m]]*Hypergeometric2F1[- m, b, b - c - m + 1, 1 - z]=Divide[Subscript[c - b, m],Subscript[c, m]]*(z)^(m)* Hypergeometric2F1[- m, 1 - c - m, b - c - m + 1, 1 -Divide[1,z]] Failure Failure Skip Skip
15.8.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{2b}{z} = \left(1-\tfrac{1}{2}z\right)^{-a}\hyperF@@{\tfrac{1}{2}a}{\tfrac{1}{2}a+\tfrac{1}{2}}{b+\tfrac{1}{2}}{\left(\frac{z}{2-z}\right)^{2}}} hypergeom([a, b], [2*b], z)=(1 -(1)/(2)*z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a +(1)/(2)], [b +(1)/(2)], ((z)/(2 - z))^(2)) Hypergeometric2F1[a, b, 2*b, z]=(1 -Divide[1,2]*z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a +Divide[1,2], b +Divide[1,2], (Divide[z,2 - z])^(2)] Failure Failure Skip Skip
15.8.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{2b}{z} = \left(1-z\right)^{-\ifrac{a}{2}}\hyperF@@{\tfrac{1}{2}a}{b-\tfrac{1}{2}a}{b+\tfrac{1}{2}}{\frac{z^{2}}{4z-4}}} hypergeom([a, b], [2*b], z)=(1 - z)^(-(a)/(2))* hypergeom([(1)/(2)*a, b -(1)/(2)*a], [b +(1)/(2)], ((z)^(2))/(4*z - 4)) Hypergeometric2F1[a, b, 2*b, z]=(1 - z)^(-Divide[a,2])* Hypergeometric2F1[Divide[1,2]*a, b -Divide[1,2]*a, b +Divide[1,2], Divide[(z)^(2),4*z - 4]] Failure Failure Skip Successful
15.8.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{a-b+1}{z} = (1+z)^{-a}\hyperF@@{\frac{1}{2}a}{\frac{1}{2}a+\frac{1}{2}}{a-b+1}{\frac{4z}{(1+z)^{2}}}} hypergeom([a, b], [a - b + 1], z)=(1 + z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a +(1)/(2)], [a - b + 1], (4*z)/((1 + z)^(2))) Hypergeometric2F1[a, b, a - b + 1, z]=(1 + z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a +Divide[1,2], a - b + 1, Divide[4*z,(1 + z)^(2)]] Failure Failure Successful Successful
15.8.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{a-b+1}{z} = (1-z)^{-a}\hyperF@@{\frac{1}{2}a}{\frac{1}{2}a-b+\frac{1}{2}}{a-b+1}{\frac{-4z}{(1-z)^{2}}}} hypergeom([a, b], [a - b + 1], z)=(1 - z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a - b +(1)/(2)], [a - b + 1], (- 4*z)/((1 - z)^(2))) Hypergeometric2F1[a, b, a - b + 1, z]=(1 - z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a - b +Divide[1,2], a - b + 1, Divide[- 4*z,(1 - z)^(2)]] Failure Failure Successful Successful
15.8.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{\frac{1}{2}(a+b+1)}{z} = (1-2z)^{-a}\hyperF@@{\frac{1}{2}a}{\frac{1}{2}a+\frac{1}{2}}{\frac{1}{2}(a+b+1)}{\frac{4z(z-1)}{(1-2z)^{2}}}} hypergeom([a, b], [(1)/(2)*(a + b + 1)], z)=(1 - 2*z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a +(1)/(2)], [(1)/(2)*(a + b + 1)], (4*z*(z - 1))/((1 - 2*z)^(2))) Hypergeometric2F1[a, b, Divide[1,2]*(a + b + 1), z]=(1 - 2*z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a +Divide[1,2], Divide[1,2]*(a + b + 1), Divide[4*z*(z - 1),(1 - 2*z)^(2)]] Failure Failure Successful Successful
15.8.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{\frac{1}{2}(a+b+1)}{z} = \hyperF@@{\frac{1}{2}a}{\frac{1}{2}b}{\frac{1}{2}(a+b+1)}{4z(1-z)}} hypergeom([a, b], [(1)/(2)*(a + b + 1)], z)= hypergeom([(1)/(2)*a, (1)/(2)*b], [(1)/(2)*(a + b + 1)], 4*z*(1 - z)) Hypergeometric2F1[a, b, Divide[1,2]*(a + b + 1), z]= Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*b, Divide[1,2]*(a + b + 1), 4*z*(1 - z)] Failure Failure Successful Successful
15.8.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{1-a}{c}{z} = (1-2z)^{1-a-c}(1-z)^{c-1}\hyperF@@{\frac{1}{2}(a+c)}{\frac{1}{2}(a+c-1)}{c}{\frac{4z(z-1)}{(1-2z)^{2}}}} hypergeom([a, 1 - a], [c], z)=(1 - 2*z)^(1 - a - c)*(1 - z)^(c - 1)* hypergeom([(1)/(2)*(a + c), (1)/(2)*(a + c - 1)], [c], (4*z*(z - 1))/((1 - 2*z)^(2))) Hypergeometric2F1[a, 1 - a, c, z]=(1 - 2*z)^(1 - a - c)*(1 - z)^(c - 1)* Hypergeometric2F1[Divide[1,2]*(a + c), Divide[1,2]*(a + c - 1), c, Divide[4*z*(z - 1),(1 - 2*z)^(2)]] Failure Failure Successful Successful
15.8.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{1-a}{c}{z} = (1-z)^{c-1}\hyperF@@{\frac{1}{2}(c-a)}{\frac{1}{2}(a+c-1)}{c}{4z(1-z)}} hypergeom([a, 1 - a], [c], z)=(1 - z)^(c - 1)* hypergeom([(1)/(2)*(c - a), (1)/(2)*(a + c - 1)], [c], 4*z*(1 - z)) Hypergeometric2F1[a, 1 - a, c, z]=(1 - z)^(c - 1)* Hypergeometric2F1[Divide[1,2]*(c - a), Divide[1,2]*(a + c - 1), c, 4*z*(1 - z)] Failure Failure Successful Successful
15.8.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{a-b+1}{z} = \left(1+\sqrt{z}\right)^{-2a}\hyperF@@{a}{a-b+\tfrac{1}{2}}{2a-2b+1}{\frac{4\sqrt{z}}{(1+\sqrt{z})^{2}}}} hypergeom([a, b], [a - b + 1], z)=(1 +sqrt(z))^(- 2*a)* hypergeom([a, a - b +(1)/(2)], [2*a - 2*b + 1], (4*sqrt(z))/((1 +sqrt(z))^(2))) Hypergeometric2F1[a, b, a - b + 1, z]=(1 +Sqrt[z])^(- 2*a)* Hypergeometric2F1[a, a - b +Divide[1,2], 2*a - 2*b + 1, Divide[4*Sqrt[z],(1 +Sqrt[z])^(2)]] Failure Failure Error Error
15.8.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{\tfrac{1}{2}(a+b+1)}{z} = \left(\frac{\sqrt{1-z^{-1}}-1}{\sqrt{1-z^{-1}}+1}\right)^{a}\hyperF@@{a}{\tfrac{1}{2}(a+b)}{a+b}{\frac{4\sqrt{1-z^{-1}}}{\left(\sqrt{1-z^{-1}}+1\right)^{2}}}} hypergeom([a, b], [(1)/(2)*(a + b + 1)], z)=((sqrt(1 - (z)^(- 1))- 1)/(sqrt(1 - (z)^(- 1))+ 1))^(a)* hypergeom([a, (1)/(2)*(a + b)], [a + b], (4*sqrt(1 - (z)^(- 1)))/((sqrt(1 - (z)^(- 1))+ 1)^(2))) Hypergeometric2F1[a, b, Divide[1,2]*(a + b + 1), z]=(Divide[Sqrt[1 - (z)^(- 1)]- 1,Sqrt[1 - (z)^(- 1)]+ 1])^(a)* Hypergeometric2F1[a, Divide[1,2]*(a + b), a + b, Divide[4*Sqrt[1 - (z)^(- 1)],(Sqrt[1 - (z)^(- 1)]+ 1)^(2)]] Failure Failure Skip Successful
15.8.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{1-a}{c}{z} = \left(\sqrt{1-z^{-1}}-1\right)^{1-a}\left(\sqrt{1-z^{-1}}+1\right)^{a-2c+1}\left(1-z^{-1}\right)^{c-1}\hyperF@@{c-a}{c-\tfrac{1}{2}}{2c-1}{\frac{4\sqrt{1-z^{-1}}}{\left(\sqrt{1-z^{-1}}+1\right)^{2}}}} hypergeom([a, 1 - a], [c], z)=(sqrt(1 - (z)^(- 1))- 1)^(1 - a)*(sqrt(1 - (z)^(- 1))+ 1)^(a - 2*c + 1)*(1 - (z)^(- 1))^(c - 1)* hypergeom([c - a, c -(1)/(2)], [2*c - 1], (4*sqrt(1 - (z)^(- 1)))/((sqrt(1 - (z)^(- 1))+ 1)^(2))) Hypergeometric2F1[a, 1 - a, c, z]=(Sqrt[1 - (z)^(- 1)]- 1)^(1 - a)*(Sqrt[1 - (z)^(- 1)]+ 1)^(a - 2*c + 1)*(1 - (z)^(- 1))^(c - 1)* Hypergeometric2F1[c - a, c -Divide[1,2], 2*c - 1, Divide[4*Sqrt[1 - (z)^(- 1)],(Sqrt[1 - (z)^(- 1)]+ 1)^(2)]] Failure Failure Skip Successful
15.8.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{a-b+1}{z} = (1-z)^{-a}\frac{\EulerGamma@{a-b+1}\EulerGamma@{\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}a-b+1}}\hyperF@@{\tfrac{1}{2}a}{\tfrac{1}{2}a-b+\tfrac{1}{2}}{\tfrac{1}{2}}{\left(\frac{z+1}{z-1}\right)^{2}}+(1+z)(1-z)^{-a-1}\frac{\EulerGamma@{a-b+1}\EulerGamma@{-\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}a}\EulerGamma@{\tfrac{1}{2}a-b+\tfrac{1}{2}}}\hyperF@@{\tfrac{1}{2}a+\tfrac{1}{2}}{\tfrac{1}{2}a-b+1}{\tfrac{3}{2}}{\left(\frac{z+1}{z-1}\right)^{2}}} hypergeom([a, b], [a - b + 1], z)=(1 - z)^(- a)*(GAMMA(a - b + 1)*GAMMA((1)/(2)))/(GAMMA((1)/(2)*a +(1)/(2))*GAMMA((1)/(2)*a - b + 1))*hypergeom([(1)/(2)*a, (1)/(2)*a - b +(1)/(2)], [(1)/(2)], ((z + 1)/(z - 1))^(2))+(1 + z)*(1 - z)^(- a - 1)*(GAMMA(a - b + 1)*GAMMA(-(1)/(2)))/(GAMMA((1)/(2)*a)*GAMMA((1)/(2)*a - b +(1)/(2)))*hypergeom([(1)/(2)*a +(1)/(2), (1)/(2)*a - b + 1], [(3)/(2)], ((z + 1)/(z - 1))^(2)) Hypergeometric2F1[a, b, a - b + 1, z]=(1 - z)^(- a)*Divide[Gamma[a - b + 1]*Gamma[Divide[1,2]],Gamma[Divide[1,2]*a +Divide[1,2]]*Gamma[Divide[1,2]*a - b + 1]]*Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a - b +Divide[1,2], Divide[1,2], (Divide[z + 1,z - 1])^(2)]+(1 + z)*(1 - z)^(- a - 1)*Divide[Gamma[a - b + 1]*Gamma[-Divide[1,2]],Gamma[Divide[1,2]*a]*Gamma[Divide[1,2]*a - b +Divide[1,2]]]*Hypergeometric2F1[Divide[1,2]*a +Divide[1,2], Divide[1,2]*a - b + 1, Divide[3,2], (Divide[z + 1,z - 1])^(2)] Failure Failure Skip Skip
15.8.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{\tfrac{1}{2}(a+b+1)}{z} = \frac{\EulerGamma@{\tfrac{1}{2}(a+b+1)}\EulerGamma@{\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}a+\tfrac{1}{2}}\EulerGamma@{\tfrac{1}{2}b+\tfrac{1}{2}}}\hyperF@@{\tfrac{1}{2}a}{\tfrac{1}{2}b}{\tfrac{1}{2}}{(1-2z)^{2}}+(1-2z)\frac{\EulerGamma@{\tfrac{1}{2}(a+b+1)}\EulerGamma@{-\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}a}\EulerGamma@{\tfrac{1}{2}b}}\hyperF@@{\tfrac{1}{2}a+\tfrac{1}{2}}{\tfrac{1}{2}b+\tfrac{1}{2}}{\tfrac{3}{2}}{(1-2z)^{2}}} hypergeom([a, b], [(1)/(2)*(a + b + 1)], z)=(GAMMA((1)/(2)*(a + b + 1))*GAMMA((1)/(2)))/(GAMMA((1)/(2)*a +(1)/(2))*GAMMA((1)/(2)*b +(1)/(2)))*hypergeom([(1)/(2)*a, (1)/(2)*b], [(1)/(2)], (1 - 2*z)^(2))+(1 - 2*z)*(GAMMA((1)/(2)*(a + b + 1))*GAMMA(-(1)/(2)))/(GAMMA((1)/(2)*a)*GAMMA((1)/(2)*b))*hypergeom([(1)/(2)*a +(1)/(2), (1)/(2)*b +(1)/(2)], [(3)/(2)], (1 - 2*z)^(2)) Hypergeometric2F1[a, b, Divide[1,2]*(a + b + 1), z]=Divide[Gamma[Divide[1,2]*(a + b + 1)]*Gamma[Divide[1,2]],Gamma[Divide[1,2]*a +Divide[1,2]]*Gamma[Divide[1,2]*b +Divide[1,2]]]*Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*b, Divide[1,2], (1 - 2*z)^(2)]+(1 - 2*z)*Divide[Gamma[Divide[1,2]*(a + b + 1)]*Gamma[-Divide[1,2]],Gamma[Divide[1,2]*a]*Gamma[Divide[1,2]*b]]*Hypergeometric2F1[Divide[1,2]*a +Divide[1,2], Divide[1,2]*b +Divide[1,2], Divide[3,2], (1 - 2*z)^(2)] Failure Failure Skip Skip
15.8.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{1-a}{c}{z} = (1-z)^{c-1}\frac{\EulerGamma@{c}\EulerGamma@{\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}(c-a+1)}\EulerGamma@{\tfrac{1}{2}c+\tfrac{1}{2}a}}\hyperF@@{\tfrac{1}{2}c-\tfrac{1}{2}a}{\tfrac{1}{2}c+\tfrac{1}{2}a-\tfrac{1}{2}}{\tfrac{1}{2}}{(1-2z)^{2}}+(1-2z)(1-z)^{c-1}\frac{\EulerGamma@{c}\EulerGamma@{-\tfrac{1}{2}}}{\EulerGamma@{\tfrac{1}{2}c-\tfrac{1}{2}a}\EulerGamma@{\tfrac{1}{2}(c+a-1)}}\hyperF@@{\tfrac{1}{2}c-\tfrac{1}{2}a+\tfrac{1}{2}}{\tfrac{1}{2}c+\tfrac{1}{2}a}{\tfrac{3}{2}}{(1-2z)^{2}}} hypergeom([a, 1 - a], [c], z)=(1 - z)^(c - 1)*(GAMMA(c)*GAMMA((1)/(2)))/(GAMMA((1)/(2)*(c - a + 1))*GAMMA((1)/(2)*c +(1)/(2)*a))*hypergeom([(1)/(2)*c -(1)/(2)*a, (1)/(2)*c +(1)/(2)*a -(1)/(2)], [(1)/(2)], (1 - 2*z)^(2))+(1 - 2*z)*(1 - z)^(c - 1)*(GAMMA(c)*GAMMA(-(1)/(2)))/(GAMMA((1)/(2)*c -(1)/(2)*a)*GAMMA((1)/(2)*(c + a - 1)))*hypergeom([(1)/(2)*c -(1)/(2)*a +(1)/(2), (1)/(2)*c +(1)/(2)*a], [(3)/(2)], (1 - 2*z)^(2)) Hypergeometric2F1[a, 1 - a, c, z]=(1 - z)^(c - 1)*Divide[Gamma[c]*Gamma[Divide[1,2]],Gamma[Divide[1,2]*(c - a + 1)]*Gamma[Divide[1,2]*c +Divide[1,2]*a]]*Hypergeometric2F1[Divide[1,2]*c -Divide[1,2]*a, Divide[1,2]*c +Divide[1,2]*a -Divide[1,2], Divide[1,2], (1 - 2*z)^(2)]+(1 - 2*z)*(1 - z)^(c - 1)*Divide[Gamma[c]*Gamma[-Divide[1,2]],Gamma[Divide[1,2]*c -Divide[1,2]*a]*Gamma[Divide[1,2]*(c + a - 1)]]*Hypergeometric2F1[Divide[1,2]*c -Divide[1,2]*a +Divide[1,2], Divide[1,2]*c +Divide[1,2]*a, Divide[3,2], (1 - 2*z)^(2)] Failure Failure Skip Successful
15.8.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2\EulerGamma@{\tfrac{1}{2}}\EulerGamma@{a+b+\tfrac{1}{2}}}{\EulerGamma@{a+\tfrac{1}{2}}\EulerGamma@{b+\tfrac{1}{2}}}\hyperF@{a}{b}{\tfrac{1}{2}}{z} = \hyperF@{2a}{2b}{a+b+\tfrac{1}{2}}{\tfrac{1}{2}-\tfrac{1}{2}\sqrt{z}}+\hyperF@{2a}{2b}{a+b+\tfrac{1}{2}}{\tfrac{1}{2}+\tfrac{1}{2}\sqrt{z}}} (2*GAMMA((1)/(2))*GAMMA(a + b +(1)/(2)))/(GAMMA(a +(1)/(2))*GAMMA(b +(1)/(2)))*hypergeom([a, b], [(1)/(2)], z)= hypergeom([2*a, 2*b], [a + b +(1)/(2)], (1)/(2)-(1)/(2)*sqrt(z))+ hypergeom([2*a, 2*b], [a + b +(1)/(2)], (1)/(2)+(1)/(2)*sqrt(z)) Divide[2*Gamma[Divide[1,2]]*Gamma[a + b +Divide[1,2]],Gamma[a +Divide[1,2]]*Gamma[b +Divide[1,2]]]*Hypergeometric2F1[a, b, Divide[1,2], z]= Hypergeometric2F1[2*a, 2*b, a + b +Divide[1,2], Divide[1,2]-Divide[1,2]*Sqrt[z]]+ Hypergeometric2F1[2*a, 2*b, a + b +Divide[1,2], Divide[1,2]+Divide[1,2]*Sqrt[z]] Failure Failure Skip Skip
15.8.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2\sqrt{z}\EulerGamma@{-\tfrac{1}{2}}\EulerGamma@{a+b-\tfrac{1}{2}}}{\EulerGamma@{a-\tfrac{1}{2}}\EulerGamma@{b-\tfrac{1}{2}}}\hyperF@{a}{b}{\tfrac{3}{2}}{z} = \hyperF@{2a-1}{2b-1}{a+b-\tfrac{1}{2}}{\tfrac{1}{2}-\tfrac{1}{2}\sqrt{z}}-\hyperF@{2a-1}{2b-1}{a+b-\tfrac{1}{2}}{\tfrac{1}{2}+\tfrac{1}{2}\sqrt{z}}} (2*sqrt(z)*GAMMA(-(1)/(2))*GAMMA(a + b -(1)/(2)))/(GAMMA(a -(1)/(2))*GAMMA(b -(1)/(2)))*hypergeom([a, b], [(3)/(2)], z)= hypergeom([2*a - 1, 2*b - 1], [a + b -(1)/(2)], (1)/(2)-(1)/(2)*sqrt(z))- hypergeom([2*a - 1, 2*b - 1], [a + b -(1)/(2)], (1)/(2)+(1)/(2)*sqrt(z)) Divide[2*Sqrt[z]*Gamma[-Divide[1,2]]*Gamma[a + b -Divide[1,2]],Gamma[a -Divide[1,2]]*Gamma[b -Divide[1,2]]]*Hypergeometric2F1[a, b, Divide[3,2], z]= Hypergeometric2F1[2*a - 1, 2*b - 1, a + b -Divide[1,2], Divide[1,2]-Divide[1,2]*Sqrt[z]]- Hypergeometric2F1[2*a - 1, 2*b - 1, a + b -Divide[1,2], Divide[1,2]+Divide[1,2]*Sqrt[z]] Failure Failure Skip Skip
15.8.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{\tfrac{1}{3}a+\tfrac{1}{3}}{\tfrac{2}{3}a+\tfrac{2}{3}}{z} = \left(1+\sqrt{z}\right)^{-2a}\*\hyperF@@{a}{\tfrac{2}{3}a+\tfrac{1}{6}}{\tfrac{4}{3}a+\tfrac{1}{3}}{\frac{4\sqrt{z}}{(1+\sqrt{z})^{2}}}} hypergeom([a, (1)/(3)*a +(1)/(3)], [(2)/(3)*a +(2)/(3)], z)=(1 +sqrt(z))^(- 2*a)* hypergeom([a, (2)/(3)*a +(1)/(6)], [(4)/(3)*a +(1)/(3)], (4*sqrt(z))/((1 +sqrt(z))^(2))) Hypergeometric2F1[a, Divide[1,3]*a +Divide[1,3], Divide[2,3]*a +Divide[2,3], z]=(1 +Sqrt[z])^(- 2*a)* Hypergeometric2F1[a, Divide[2,3]*a +Divide[1,6], Divide[4,3]*a +Divide[1,3], Divide[4*Sqrt[z],(1 +Sqrt[z])^(2)]] Failure Failure
Fail
1.372516024+1.825805270*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.6051524755-3.068921398*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.2975793921-.5999898475*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.990518232e-1-9.951495097*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[1.372516027919868, 1.8258052682131423] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6051524788001073, -3.068921398743132] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.29757939171102116, -0.5999898475376467] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.09905183258496669, -9.951495092476645] <- {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
15.8.E30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}z\right)^{-a}\hyperF@@{\tfrac{1}{2}a}{\tfrac{1}{2}a+\tfrac{1}{2}}{\tfrac{1}{3}a+\tfrac{5}{6}}{\left(\frac{z}{2-z}\right)^{2}} = \hyperF@@{a}{\tfrac{1}{3}a+\tfrac{1}{3}}{\tfrac{2}{3}a+\tfrac{2}{3}}{z}} (1 -(1)/(2)*z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a +(1)/(2)], [(1)/(3)*a +(5)/(6)], ((z)/(2 - z))^(2))= hypergeom([a, (1)/(3)*a +(1)/(3)], [(2)/(3)*a +(2)/(3)], z) (1 -Divide[1,2]*z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a +Divide[1,2], Divide[1,3]*a +Divide[5,6], (Divide[z,2 - z])^(2)]= Hypergeometric2F1[a, Divide[1,3]*a +Divide[1,3], Divide[2,3]*a +Divide[2,3], z] Failure Failure Successful Successful
15.8.E30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{\tfrac{1}{3}a+\tfrac{1}{3}}{\tfrac{2}{3}a+\tfrac{2}{3}}{z} = (1+z)^{-a}\hyperF@@{\tfrac{1}{2}a}{\tfrac{1}{2}a+\tfrac{1}{2}}{\tfrac{2}{3}a+\tfrac{2}{3}}{\frac{4z}{(1+z)^{2}}}} hypergeom([a, (1)/(3)*a +(1)/(3)], [(2)/(3)*a +(2)/(3)], z)=(1 + z)^(- a)* hypergeom([(1)/(2)*a, (1)/(2)*a +(1)/(2)], [(2)/(3)*a +(2)/(3)], (4*z)/((1 + z)^(2))) Hypergeometric2F1[a, Divide[1,3]*a +Divide[1,3], Divide[2,3]*a +Divide[2,3], z]=(1 + z)^(- a)* Hypergeometric2F1[Divide[1,2]*a, Divide[1,2]*a +Divide[1,2], Divide[2,3]*a +Divide[2,3], Divide[4*z,(1 + z)^(2)]] Failure Failure
Fail
1.372516027+1.825805270*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.6051524754-3.068921398*I <- {a = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.2975793922-.5999898476*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.990518493e-1-9.951495087*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[1.372516027919873, 1.825805268213136] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.605152478800107, -3.0689213987431314] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.2975793917110212, -0.5999898475376467] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.09905183258496181, -9.951495092476698] <- {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
15.8.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{3a}{3a+\frac{1}{2}}{4a+\frac{2}{3}}{z} = \left(1-\tfrac{9}{8}z\right)^{-2a}\*\hyperF@@{a}{a+\frac{1}{2}}{2a+\frac{5}{6}}{\frac{27z^{2}(z-1)}{(9z-8)^{2}}}} hypergeom([3*a, 3*a +(1)/(2)], [4*a +(2)/(3)], z)=(1 -(9)/(8)*z)^(- 2*a)* hypergeom([a, a +(1)/(2)], [2*a +(5)/(6)], (27*(z)^(2)*(z - 1))/((9*z - 8)^(2))) Hypergeometric2F1[3*a, 3*a +Divide[1,2], 4*a +Divide[2,3], z]=(1 -Divide[9,8]*z)^(- 2*a)* Hypergeometric2F1[a, a +Divide[1,2], 2*a +Divide[5,6], Divide[27*(z)^(2)*(z - 1),(9*z - 8)^(2)]] Failure Failure Successful Successful
15.8.E32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\left(1-z^{3}\right)^{a}}{\left(-z\right)^{3a}}\left(\frac{1}{\EulerGamma@{a+\frac{2}{3}}\EulerGamma@{\frac{2}{3}}}\hyperF@@{a}{a+\frac{1}{3}}{\frac{2}{3}}{z^{-3}}+\frac{e^{\frac{1}{3}\pi\iunit}}{z\EulerGamma@{a}\EulerGamma@{\frac{4}{3}}}\hyperF@@{a+\frac{1}{3}}{a+\frac{2}{3}}{\frac{4}{3}}{z^{-3}}\right) = \frac{3^{\frac{3}{2}a+\frac{1}{2}}e^{\frac{1}{2}a\pi\iunit}\EulerGamma@{a+\frac{1}{3}}(1-\zeta)^{a}}{2\pi\EulerGamma@{2a+\frac{2}{3}}(-\zeta)^{2a}}\hyperF@@{a+\frac{1}{3}}{3a}{2a+\frac{2}{3}}{\zeta^{-1}}} ((1 - (z)^(3))^(a))/((- z)^(3*a))*((1)/(GAMMA(a +(2)/(3))*GAMMA((2)/(3)))*hypergeom([a, a +(1)/(3)], [(2)/(3)], (z)^(- 3))+(exp((1)/(3)*Pi*I))/(z*GAMMA(a)*GAMMA((4)/(3)))*hypergeom([a +(1)/(3), a +(2)/(3)], [(4)/(3)], (z)^(- 3)))=((3)^((3)/(2)*a +(1)/(2))* exp((1)/(2)*a*Pi*I)*GAMMA(a +(1)/(3))*(1 - zeta)^(a))/(2*Pi*GAMMA(2*a +(2)/(3))*(- zeta)^(2*a))*hypergeom([a +(1)/(3), 3*a], [2*a +(2)/(3)], (zeta)^(- 1)) Divide[(1 - (z)^(3))^(a),(- z)^(3*a)]*(Divide[1,Gamma[a +Divide[2,3]]*Gamma[Divide[2,3]]]*Hypergeometric2F1[a, a +Divide[1,3], Divide[2,3], (z)^(- 3)]+Divide[Exp[Divide[1,3]*Pi*I],z*Gamma[a]*Gamma[Divide[4,3]]]*Hypergeometric2F1[a +Divide[1,3], a +Divide[2,3], Divide[4,3], (z)^(- 3)])=Divide[(3)^(Divide[3,2]*a +Divide[1,2])* Exp[Divide[1,2]*a*Pi*I]*Gamma[a +Divide[1,3]]*(1 - \[zeta])^(a),2*Pi*Gamma[2*a +Divide[2,3]]*(- \[zeta])^(2*a)]*Hypergeometric2F1[a +Divide[1,3], 3*a, 2*a +Divide[2,3], (\[zeta])^(- 1)] Failure Failure Error Error
15.8.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{\frac{1}{3}}{\frac{2}{3}}{1}{1-\left(\frac{1-z}{1+2z}\right)^{3}} = (1+2z)\hyperF@@{\frac{1}{3}}{\frac{2}{3}}{1}{z^{3}}} hypergeom([(1)/(3), (2)/(3)], [1], 1 -((1 - z)/(1 + 2*z))^(3))=(1 + 2*z)* hypergeom([(1)/(3), (2)/(3)], [1], (z)^(3)) Hypergeometric2F1[Divide[1,3], Divide[2,3], 1, 1 -(Divide[1 - z,1 + 2*z])^(3)]=(1 + 2*z)* Hypergeometric2F1[Divide[1,3], Divide[2,3], 1, (z)^(3)] Failure Failure
Fail
-.10742540e-1-1.736124843*I <- {z = 2^(1/2)+I*2^(1/2)}
-.10742540e-1+1.736124843*I <- {z = 2^(1/2)-I*2^(1/2)}
3.107241801+.4009013497*I <- {z = -2^(1/2)-I*2^(1/2)}
3.107241801-.4009013497*I <- {z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[-0.010742539950905128, -1.7361248428967333] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.010742539950905128, 1.7361248428967333] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.107241800778924, 0.40090134898439433] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.107241800778924, -0.40090134898439433] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
15.9.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobipolyP{\alpha}{\beta}{n}@{x} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\hyperF@@{-n}{n+\alpha+\beta+1}{\alpha+1}{\frac{1-x}{2}}} JacobiP(n, alpha, beta, x)=(pochhammer(alpha + 1, n))/(factorial(n))*hypergeom([- n, n + alpha + beta + 1], [alpha + 1], (1 - x)/(2)) JacobiP[n, \[Alpha], \[Beta], x]=Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*Hypergeometric2F1[- n, n + \[Alpha]+ \[Beta]+ 1, \[Alpha]+ 1, Divide[1 - x,2]] Successful Successful - -
15.9.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{n!}\hyperF@@{-n}{n+2\lambda}{\lambda+\frac{1}{2}}{\frac{1-x}{2}}} GegenbauerC(n, lambda, x)=(pochhammer(2*lambda, n))/(factorial(n))*hypergeom([- n, n + 2*lambda], [lambda +(1)/(2)], (1 - x)/(2)) GegenbauerC[n, \[Lambda], x]=Divide[Pochhammer[2*\[Lambda], n],(n)!]*Hypergeometric2F1[- n, n + 2*\[Lambda], \[Lambda]+Divide[1,2], Divide[1 - x,2]] Successful Successful - -
15.9.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{x} = (2x)^{n}\frac{\Pochhammersym{\lambda}{n}}{n!}\hyperF@@{-\frac{1}{2}n}{\frac{1}{2}(1-n)}{1-\lambda-n}{\frac{1}{x^{2}}}} GegenbauerC(n, lambda, x)=(2*x)^(n)*(pochhammer(lambda, n))/(factorial(n))*hypergeom([-(1)/(2)*n, (1)/(2)*(1 - n)], [1 - lambda - n], (1)/((x)^(2))) GegenbauerC[n, \[Lambda], x]=(2*x)^(n)*Divide[Pochhammer[\[Lambda], n],(n)!]*Hypergeometric2F1[-Divide[1,2]*n, Divide[1,2]*(1 - n), 1 - \[Lambda]- n, Divide[1,(x)^(2)]] Failure Failure Successful Successful
15.9.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{\cos@@{\theta}} = e^{n\iunit\theta}\frac{\Pochhammersym{\lambda}{n}}{n!}\hyperF@@{-n}{\lambda}{1-\lambda-n}{e^{-2\iunit\theta}}} GegenbauerC(n, lambda, cos(theta))= exp(n*I*theta)*(pochhammer(lambda, n))/(factorial(n))*hypergeom([- n, lambda], [1 - lambda - n], exp(- 2*I*theta)) GegenbauerC[n, \[Lambda], Cos[\[Theta]]]= Exp[n*I*\[Theta]]*Divide[Pochhammer[\[Lambda], n],(n)!]*Hypergeometric2F1[- n, \[Lambda], 1 - \[Lambda]- n, Exp[- 2*I*\[Theta]]] Failure Failure Successful Successful
15.9.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n}@{x} = \hyperF@@{-n}{n}{\frac{1}{2}}{\frac{1-x}{2}}} ChebyshevT(n, x)= hypergeom([- n, n], [(1)/(2)], (1 - x)/(2)) ChebyshevT[n, x]= Hypergeometric2F1[- n, n, Divide[1,2], Divide[1 - x,2]] Successful Successful - -
15.9.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{n}@{x} = (n+1)\hyperF@@{-n}{n+2}{\frac{3}{2}}{\frac{1-x}{2}}} ChebyshevU(n, x)=(n + 1)* hypergeom([- n, n + 2], [(3)/(2)], (1 - x)/(2)) ChebyshevU[n, x]=(n + 1)* Hypergeometric2F1[- n, n + 2, Divide[3,2], Divide[1 - x,2]] Successful Failure - Successful
15.9.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{n}@{x} = \hyperF@@{-n}{n+1}{1}{\frac{1-x}{2}}} LegendreP(n, x)= hypergeom([- n, n + 1], [1], (1 - x)/(2)) LegendreP[n, x]= Hypergeometric2F1[- n, n + 1, 1, Divide[1 - x,2]] Successful Successful - -
15.9.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiphi{\alpha}{\beta}{\lambda}@{t} = \hyperF@@{\tfrac{1}{2}(\alpha+\beta+1-\iunit\lambda)}{\tfrac{1}{2}(\alpha+\beta+1+\iunit\lambda)}{\alpha+1}{-\sinh^{2}@@{t}}} hypergeom([((alpha)+(beta)+1-I*(lambda))/2, ((alpha)+(beta)+1+I*(lambda))], [(alpha)+1], -sinh(t)^2)= hypergeom([(1)/(2)*(alpha + beta + 1 - I*lambda), (1)/(2)*(alpha + beta + 1 + I*lambda)], [alpha + 1], - (sinh(t))^(2)) Error Failure Error
Fail
1042.578545-886.9426609*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2)}
.4942284159e-3+.1205933063e-2*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), t = 2^(1/2)-I*2^(1/2)}
1042.578545-886.9426609*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), t = -2^(1/2)-I*2^(1/2)}
.4942284159e-3+.1205933063e-2*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), t = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 -
15.9.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{\alpha}@{z} = \frac{\EulerGamma@{\alpha+2\lambda}}{\EulerGamma@{2\lambda}\EulerGamma@{\alpha+1}}\hyperF@@{-\alpha}{\alpha+2\lambda}{\lambda+\tfrac{1}{2}}{\frac{1-z}{2}}} GegenbauerC(alpha, lambda, z)=(GAMMA(alpha + 2*lambda))/(GAMMA(2*lambda)*GAMMA(alpha + 1))*hypergeom([- alpha, alpha + 2*lambda], [lambda +(1)/(2)], (1 - z)/(2)) GegenbauerC[\[Alpha], \[Lambda], z]=Divide[Gamma[\[Alpha]+ 2*\[Lambda]],Gamma[2*\[Lambda]]*Gamma[\[Alpha]+ 1]]*Hypergeometric2F1[- \[Alpha], \[Alpha]+ 2*\[Lambda], \[Lambda]+Divide[1,2], Divide[1 - z,2]] Successful Successful - -
15.9.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{2b}{z} = \frac{\sqrt{\pi}}{\EulerGamma@{b}}z^{-b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2}\*\assLegendreP[-b+(\ifrac{1}{2})]{a-b-(\ifrac{1}{2})}@{\frac{2-z}{2\sqrt{1-z}}}} hypergeom([a, b], [2*b], z)/GAMMA(2*b)=(sqrt(Pi))/(GAMMA(b))*(z)^(- b +((1)/(2)))*(1 - z)^((b - a -((1)/(2)))/ 2)* LegendreP(a - b -((1)/(2)), - b +((1)/(2)), (2 - z)/(2*sqrt(1 - z))) Hypergeometric2F1Regularized[a, b, 2*b, z]=Divide[Sqrt[Pi],Gamma[b]]*(z)^(- b +(Divide[1,2]))*(1 - z)^((b - a -(Divide[1,2]))/ 2)* LegendreP[a - b -(Divide[1,2]), - b +(Divide[1,2]), 3, Divide[2 - z,2*Sqrt[1 - z]]] Failure Failure Error Error
15.9.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{a+\tfrac{1}{2}}{c}{z} = 2^{c-1}z^{\ifrac{(1-c)}{2}}(1-z)^{-a+(\ifrac{(c-1)}{2})}\*\assLegendreP[1-c]{2a-c}@{\frac{1}{\sqrt{1-z}}}} hypergeom([a, a +(1)/(2)], [c], z)/GAMMA(c)= (2)^(c - 1)* (z)^((1 - c)/(2))*(1 - z)^(- a +((c - 1)/(2)))* LegendreP(2*a - c, 1 - c, (1)/(sqrt(1 - z))) Hypergeometric2F1Regularized[a, a +Divide[1,2], c, z]= (2)^(c - 1)* (z)^(Divide[1 - c,2])*(1 - z)^(- a +(Divide[c - 1,2]))* LegendreP[2*a - c, 1 - c, 3, Divide[1,Sqrt[1 - z]]] Failure Failure Skip Successful
15.9.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{a-b+1}{z} = z^{\ifrac{(b-a)}{2}}(1-z)^{-b}\*\assLegendreP[b-a]{-b}@{\frac{1+z}{1-z}}} hypergeom([a, b], [a - b + 1], z)/GAMMA(a - b + 1)= (z)^((b - a)/(2))*(1 - z)^(- b)* LegendreP(- b, b - a, (1 + z)/(1 - z)) Hypergeometric2F1Regularized[a, b, a - b + 1, z]= (z)^(Divide[b - a,2])*(1 - z)^(- b)* LegendreP[- b, b - a, 3, Divide[1 + z,1 - z]] Successful Failure - Successful
15.9.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{\tfrac{1}{2}(a+b+1)}{z} = \left(-z(1-z)\right)^{\ifrac{(1-a-b)}{4}}\*\assLegendreP[\ifrac{(1-a-b)}{2}]{\ifrac{(a-b-1)}{2}}@{1-2z}} hypergeom([a, b], [(1)/(2)*(a + b + 1)], z)/GAMMA((1)/(2)*(a + b + 1))=(- z*(1 - z))^((1 - a - b)/(4))* LegendreP((a - b - 1)/(2), (1 - a - b)/(2), 1 - 2*z) Hypergeometric2F1Regularized[a, b, Divide[1,2]*(a + b + 1), z]=(- z*(1 - z))^(Divide[1 - a - b,4])* LegendreP[Divide[a - b - 1,2], Divide[1 - a - b,2], 3, 1 - 2*z] Failure Failure Skip
Fail
Complex[6.0300259512809715, 8.154472102119673] <- {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[-17.372827152675953, -0.5381367643934912] <- {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[-2.4668594623806452, -1.8721092491501343] <- {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[-2.4668594623806426, 1.8721092491501325] <- {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
15.9.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{1-a}{c}{z} = \left(\frac{-z}{1-z}\right)^{\ifrac{(1-c)}{2}}\*\assLegendreP[1-c]{-a}@{1-2z}} hypergeom([a, 1 - a], [c], z)/GAMMA(c)=((- z)/(1 - z))^((1 - c)/(2))* LegendreP(- a, 1 - c, 1 - 2*z) Hypergeometric2F1Regularized[a, 1 - a, c, z]=(Divide[- z,1 - z])^(Divide[1 - c,2])* LegendreP[- a, 1 - c, 3, 1 - 2*z] Failure Successful Skip -
15.10.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)\deriv[2]{w}{z}+\left(c-(a+b+1)z\right)\deriv{w}{z}-abw = 0} z*(1 - z)* diff(w, [z$(2)])+(c -(a + b + 1)*z)* diff(w, z)- a*b*w = 0 z*(1 - z)* D[w, {z, 2}]+(c -(a + b + 1)*z)* D[w, z]- a*b*w = 0 Failure Failure
Fail
5.656854245-5.656854245*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)}
-5.656854245-5.656854245*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)}
-5.656854245+5.656854245*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)}
5.656854245+5.656854245*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)}
... skip entries to safe data
Fail
Complex[5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[b, 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
15.10#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = \hyperF@@{a}{b}{c}{z}} f[1]*(z)= hypergeom([a, b], [c], z) Subscript[f, 1]*(z)= Hypergeometric2F1[a, b, c, z] Failure Failure Skip Skip
15.10#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z) = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}} f[2]*(z)= (z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [2 - c], z) Subscript[f, 2]*(z)= (z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z] Failure Failure Skip Skip
15.10#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = \hyperF@@{a}{b}{a+b+1-c}{1-z}} f[1]*(z)= hypergeom([a, b], [a + b + 1 - c], 1 - z) Subscript[f, 1]*(z)= Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z] Failure Failure Skip Skip
15.10#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z) = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z}} f[2]*(z)=(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z) Subscript[f, 2]*(z)=(1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z] Failure Failure Skip Skip
15.10#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(z) = z^{-a}\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}} f[1]*(z)= (z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z)) Subscript[f, 1]*(z)= (z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]] Failure Failure Skip Skip
15.10#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(z) = z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}} f[2]*(z)= (z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z)) Subscript[f, 2]*(z)= (z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]] Failure Failure Skip Skip
15.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = \hyperF@@{a}{b}{c}{z}} w[1]*(z)= hypergeom([a, b], [c], z) Subscript[w, 1]*(z)= Hypergeometric2F1[a, b, c, z] Failure Failure Skip Skip
15.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{c}{z} = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z}} hypergeom([a, b], [c], z)=(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c], z) Hypergeometric2F1[a, b, c, z]=(1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c, z] Failure Successful Successful -
15.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c}{z} = (1-z)^{-a}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}}} (1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c], z)=(1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1)) (1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c, z]=(1 - z)^(- a)* Hypergeometric2F1[a, c - b, c, Divide[z,z - 1]] Failure Failure Skip Skip
15.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{-a}\hyperF@@{a}{c-b}{c}{\frac{z}{z-1}} = (1-z)^{-b}\hyperF@@{c-a}{b}{c}{\frac{z}{z-1}}} (1 - z)^(- a)* hypergeom([a, c - b], [c], (z)/(z - 1))=(1 - z)^(- b)* hypergeom([c - a, b], [c], (z)/(z - 1)) (1 - z)^(- a)* Hypergeometric2F1[a, c - b, c, Divide[z,z - 1]]=(1 - z)^(- b)* Hypergeometric2F1[c - a, b, c, Divide[z,z - 1]] Failure Failure Skip Error
15.10.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z}} w[2]*(z)=(z)^(1 - c)*hypergeom([a - c + 1, b - c + 1], [2 - c], z) Subscript[w, 2]*(z)=(z)^(1 - c)*Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z] Failure Failure Skip Error
15.10.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {z^{1-c}}\hyperF@@{a-c+1}{b-c+1}{2-c}{z} = {z^{1-c}(1-z)^{c-a-b}}\*\hyperF@@{1-a}{1-b}{2-c}{z}} (z)^(1 - c)*hypergeom([a - c + 1, b - c + 1], [2 - c], z)=(z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [2 - c], z) (z)^(1 - c)*Hypergeometric2F1[a - c + 1, b - c + 1, 2 - c, z]=(z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, 2 - c, z] Failure Successful Successful -
15.10.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {z^{1-c}(1-z)^{c-a-b}}\*\hyperF@@{1-a}{1-b}{2-c}{z} = {z^{1-c}(1-z)^{c-a-1}}\*\hyperF@@{a-c+1}{1-b}{2-c}{\frac{z}{z-1}}} (z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [2 - c], z)=(z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([a - c + 1, 1 - b], [2 - c], (z)/(z - 1)) (z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, 2 - c, z]=(z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[a - c + 1, 1 - b, 2 - c, Divide[z,z - 1]] Failure Failure Skip Skip
15.10.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {z^{1-c}(1-z)^{c-a-1}}\*\hyperF@@{a-c+1}{1-b}{2-c}{\frac{z}{z-1}} = {z^{1-c}(1-z)^{c-b-1}}\*\hyperF@@{1-a}{b-c+1}{2-c}{\frac{z}{z-1}}} (z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([a - c + 1, 1 - b], [2 - c], (z)/(z - 1))=(z)^(1 - c)*(1 - z)^(c - b - 1)* hypergeom([1 - a, b - c + 1], [2 - c], (z)/(z - 1)) (z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[a - c + 1, 1 - b, 2 - c, Divide[z,z - 1]]=(z)^(1 - c)*(1 - z)^(c - b - 1)* Hypergeometric2F1[1 - a, b - c + 1, 2 - c, Divide[z,z - 1]] Failure Failure Skip -
15.10.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{3}(z) = \hyperF@@{a}{b}{a+b-c+1}{1-z}} w[3]*(z)= hypergeom([a, b], [a + b - c + 1], 1 - z) Subscript[w, 3]*(z)= Hypergeometric2F1[a, b, a + b - c + 1, 1 - z] Failure Failure Skip Error
15.10.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{a+b-c+1}{1-z} = z^{1-c}\hyperF@@{a-c+1}{b-c+1}{a+b-c+1}{1-z}} hypergeom([a, b], [a + b - c + 1], 1 - z)= (z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [a + b - c + 1], 1 - z) Hypergeometric2F1[a, b, a + b - c + 1, 1 - z]= (z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, a + b - c + 1, 1 - z] Failure Successful Successful -
15.10.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{1-c}\hyperF@@{a-c+1}{b-c+1}{a+b-c+1}{1-z} = z^{-a}\hyperF@@{a}{a-c+1}{a+b-c+1}{1-\frac{1}{z}}} (z)^(1 - c)* hypergeom([a - c + 1, b - c + 1], [a + b - c + 1], 1 - z)= (z)^(- a)* hypergeom([a, a - c + 1], [a + b - c + 1], 1 -(1)/(z)) (z)^(1 - c)* Hypergeometric2F1[a - c + 1, b - c + 1, a + b - c + 1, 1 - z]= (z)^(- a)* Hypergeometric2F1[a, a - c + 1, a + b - c + 1, 1 -Divide[1,z]] Failure Failure Skip Skip
15.10.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-a}\hyperF@@{a}{a-c+1}{a+b-c+1}{1-\frac{1}{z}} = z^{-b}\hyperF@@{b}{b-c+1}{a+b-c+1}{1-\frac{1}{z}}} (z)^(- a)* hypergeom([a, a - c + 1], [a + b - c + 1], 1 -(1)/(z))= (z)^(- b)* hypergeom([b, b - c + 1], [a + b - c + 1], 1 -(1)/(z)) (z)^(- a)* Hypergeometric2F1[a, a - c + 1, a + b - c + 1, 1 -Divide[1,z]]= (z)^(- b)* Hypergeometric2F1[b, b - c + 1, a + b - c + 1, 1 -Divide[1,z]] Failure Failure Skip Error
15.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{4}(z) = (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z}} w[4]*(z)=(1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z) Subscript[w, 4]*(z)=(1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z] Failure Failure Skip Error
15.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{c-a-b}\hyperF@@{c-a}{c-b}{c-a-b+1}{1-z} = z^{1-c}(1-z)^{c-a-b}\hyperF@@{1-a}{1-b}{c-a-b+1}{1-z}} (1 - z)^(c - a - b)* hypergeom([c - a, c - b], [c - a - b + 1], 1 - z)= (z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [c - a - b + 1], 1 - z) (1 - z)^(c - a - b)* Hypergeometric2F1[c - a, c - b, c - a - b + 1, 1 - z]= (z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, c - a - b + 1, 1 - z] Failure Successful Successful -
15.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{1-c}(1-z)^{c-a-b}\hyperF@@{1-a}{1-b}{c-a-b+1}{1-z} = z^{a-c}(1-z)^{c-a-b}\hyperF@@{1-a}{c-a}{c-a-b+1}{1-\frac{1}{z}}} (z)^(1 - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, 1 - b], [c - a - b + 1], 1 - z)= (z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [c - a - b + 1], 1 -(1)/(z)) (z)^(1 - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, 1 - b, c - a - b + 1, 1 - z]= (z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, c - a - b + 1, 1 -Divide[1,z]] Failure Failure Skip Error
15.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{a-c}(1-z)^{c-a-b}\hyperF@@{1-a}{c-a}{c-a-b+1}{1-\frac{1}{z}} = z^{b-c}(1-z)^{c-a-b}\hyperF@@{1-b}{c-b}{c-a-b+1}{1-\frac{1}{z}}} (z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [c - a - b + 1], 1 -(1)/(z))= (z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [c - a - b + 1], 1 -(1)/(z)) (z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, c - a - b + 1, 1 -Divide[1,z]]= (z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, c - a - b + 1, 1 -Divide[1,z]] Failure Failure Skip Error
15.10.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{5}(z) = e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}}} w[5]*(z)= exp(a*Pi*I)*(z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z)) Subscript[w, 5]*(z)= Exp[a*Pi*I]*(z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]] Failure Failure Skip Error
15.10.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{a\pi\iunit}z^{-a}\*\hyperF@@{a}{a-c+1}{a-b+1}{\frac{1}{z}} = e^{(c-b)\pi\iunit}z^{b-c}(1-z)^{c-a-b}\*\hyperF@@{1-b}{c-b}{a-b+1}{\frac{1}{z}}} exp(a*Pi*I)*(z)^(- a)* hypergeom([a, a - c + 1], [a - b + 1], (1)/(z))= exp((c - b)* Pi*I)*(z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [a - b + 1], (1)/(z)) Exp[a*Pi*I]*(z)^(- a)* Hypergeometric2F1[a, a - c + 1, a - b + 1, Divide[1,z]]= Exp[(c - b)* Pi*I]*(z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, a - b + 1, Divide[1,z]] Failure Failure
Fail
7.970044489-.2486707840*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.2924289380+.3979493992*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-111204179.9-19704571.71*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
37840345.04-37561456.11*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), c = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
... skip entries to safe data
 Error
15.10.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{(c-b)\pi\iunit}z^{b-c}(1-z)^{c-a-b}\*\hyperF@@{1-b}{c-b}{a-b+1}{\frac{1}{z}} = (1-z)^{-a}\hyperF@@{a}{c-b}{a-b+1}{\frac{1}{1-z}}} exp((c - b)* Pi*I)*(z)^(b - c)*(1 - z)^(c - a - b)* hypergeom([1 - b, c - b], [a - b + 1], (1)/(z))=(1 - z)^(- a)* hypergeom([a, c - b], [a - b + 1], (1)/(1 - z)) Exp[(c - b)* Pi*I]*(z)^(b - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - b, c - b, a - b + 1, Divide[1,z]]=(1 - z)^(- a)* Hypergeometric2F1[a, c - b, a - b + 1, Divide[1,1 - z]] Failure Failure Skip Error
15.10.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{-a}\hyperF@@{a}{c-b}{a-b+1}{\frac{1}{1-z}} = e^{(c-1)\pi\iunit}z^{1-c}(1-z)^{c-a-1}\*\hyperF@@{1-b}{a-c+1}{a-b+1}{\frac{1}{1-z}}} (1 - z)^(- a)* hypergeom([a, c - b], [a - b + 1], (1)/(1 - z))= exp((c - 1)* Pi*I)*(z)^(1 - c)*(1 - z)^(c - a - 1)* hypergeom([1 - b, a - c + 1], [a - b + 1], (1)/(1 - z)) (1 - z)^(- a)* Hypergeometric2F1[a, c - b, a - b + 1, Divide[1,1 - z]]= Exp[(c - 1)* Pi*I]*(z)^(1 - c)*(1 - z)^(c - a - 1)* Hypergeometric2F1[1 - b, a - c + 1, a - b + 1, Divide[1,1 - z]] Failure Failure Skip Error
15.10.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{6}(z) = e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}}} w[6]*(z)= exp(b*Pi*I)*(z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z)) Subscript[w, 6]*(z)= Exp[b*Pi*I]*(z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]] Failure Failure - -
15.10.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{b\pi\iunit}z^{-b}\hyperF@@{b}{b-c+1}{b-a+1}{\frac{1}{z}} = e^{(c-a)\pi\iunit}z^{a-c}(1-z)^{c-a-b}\*\hyperF@@{1-a}{c-a}{b-a+1}{\frac{1}{z}}} exp(b*Pi*I)*(z)^(- b)* hypergeom([b, b - c + 1], [b - a + 1], (1)/(z))= exp((c - a)* Pi*I)*(z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [b - a + 1], (1)/(z)) Exp[b*Pi*I]*(z)^(- b)* Hypergeometric2F1[b, b - c + 1, b - a + 1, Divide[1,z]]= Exp[(c - a)* Pi*I]*(z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, b - a + 1, Divide[1,z]] Failure Failure - -
15.10.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{(c-a)\pi\iunit}z^{a-c}(1-z)^{c-a-b}\*\hyperF@@{1-a}{c-a}{b-a+1}{\frac{1}{z}} = (1-z)^{-b}\hyperF@@{b}{c-a}{b-a+1}{\frac{1}{1-z}}} exp((c - a)* Pi*I)*(z)^(a - c)*(1 - z)^(c - a - b)* hypergeom([1 - a, c - a], [b - a + 1], (1)/(z))=(1 - z)^(- b)* hypergeom([b, c - a], [b - a + 1], (1)/(1 - z)) Exp[(c - a)* Pi*I]*(z)^(a - c)*(1 - z)^(c - a - b)* Hypergeometric2F1[1 - a, c - a, b - a + 1, Divide[1,z]]=(1 - z)^(- b)* Hypergeometric2F1[b, c - a, b - a + 1, Divide[1,1 - z]] Failure Failure - -
15.10.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{-b}\hyperF@@{b}{c-a}{b-a+1}{\frac{1}{1-z}} = e^{(c-1)\pi\iunit}z^{1-c}(1-z)^{c-b-1}\*\hyperF@@{1-a}{b-c+1}{b-a+1}{\frac{1}{1-z}}} (1 - z)^(- b)* hypergeom([b, c - a], [b - a + 1], (1)/(1 - z))= exp((c - 1)* Pi*I)*(z)^(1 - c)*(1 - z)^(c - b - 1)* hypergeom([1 - a, b - c + 1], [b - a + 1], (1)/(1 - z)) (1 - z)^(- b)* Hypergeometric2F1[b, c - a, b - a + 1, Divide[1,1 - z]]= Exp[(c - 1)* Pi*I]*(z)^(1 - c)*(1 - z)^(c - b - 1)* Hypergeometric2F1[1 - a, b - c + 1, b - a + 1, Divide[1,1 - z]] Failure Failure - -
15.10.E17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{3}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{a+b-c+1}}{\EulerGamma@{a-c+1}\EulerGamma@{b-c+1}}w_{1}(z)+\frac{\EulerGamma@{c-1}\EulerGamma@{a+b-c+1}}{\EulerGamma@{a}\EulerGamma@{b}}w_{2}(z)} w[3]*(z)=(GAMMA(1 - c)*GAMMA(a + b - c + 1))/(GAMMA(a - c + 1)*GAMMA(b - c + 1))*w[1]*(z)+(GAMMA(c - 1)*GAMMA(a + b - c + 1))/(GAMMA(a)*GAMMA(b))*w[2]*(z) Subscript[w, 3]*(z)=Divide[Gamma[1 - c]*Gamma[a + b - c + 1],Gamma[a - c + 1]*Gamma[b - c + 1]]*Subscript[w, 1]*(z)+Divide[Gamma[c - 1]*Gamma[a + b - c + 1],Gamma[a]*Gamma[b]]*Subscript[w, 2]*(z) Failure Failure Skip Error
15.10.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{4}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{c-a-b+1}}{\EulerGamma@{1-a}\EulerGamma@{1-b}}w_{1}(z)+\frac{\EulerGamma@{c-1}\EulerGamma@{c-a-b+1}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}w_{2}(z)} w[4]*(z)=(GAMMA(1 - c)*GAMMA(c - a - b + 1))/(GAMMA(1 - a)*GAMMA(1 - b))*w[1]*(z)+(GAMMA(c - 1)*GAMMA(c - a - b + 1))/(GAMMA(c - a)*GAMMA(c - b))*w[2]*(z) Subscript[w, 4]*(z)=Divide[Gamma[1 - c]*Gamma[c - a - b + 1],Gamma[1 - a]*Gamma[1 - b]]*Subscript[w, 1]*(z)+Divide[Gamma[c - 1]*Gamma[c - a - b + 1],Gamma[c - a]*Gamma[c - b]]*Subscript[w, 2]*(z) Failure Failure Skip Error
15.10.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{5}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{a-b+1}}{\EulerGamma@{a-c+1}\EulerGamma@{1-b}}w_{1}(z)+e^{(c-1)\pi\iunit}\frac{\EulerGamma@{c-1}\EulerGamma@{a-b+1}}{\EulerGamma@{a}\EulerGamma@{c-b}}w_{2}(z)} w[5]*(z)=(GAMMA(1 - c)*GAMMA(a - b + 1))/(GAMMA(a - c + 1)*GAMMA(1 - b))*w[1]*(z)+ exp((c - 1)* Pi*I)*(GAMMA(c - 1)*GAMMA(a - b + 1))/(GAMMA(a)*GAMMA(c - b))*w[2]*(z) Subscript[w, 5]*(z)=Divide[Gamma[1 - c]*Gamma[a - b + 1],Gamma[a - c + 1]*Gamma[1 - b]]*Subscript[w, 1]*(z)+ Exp[(c - 1)* Pi*I]*Divide[Gamma[c - 1]*Gamma[a - b + 1],Gamma[a]*Gamma[c - b]]*Subscript[w, 2]*(z) Failure Failure Skip Error
15.10.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{6}(z) = \frac{\EulerGamma@{1-c}\EulerGamma@{b-a+1}}{\EulerGamma@{b-c+1}\EulerGamma@{1-a}}w_{1}(z)+e^{(c-1)\pi\iunit}\frac{\EulerGamma@{c-1}\EulerGamma@{b-a+1}}{\EulerGamma@{b}\EulerGamma@{c-a}}w_{2}(z)} w[6]*(z)=(GAMMA(1 - c)*GAMMA(b - a + 1))/(GAMMA(b - c + 1)*GAMMA(1 - a))*w[1]*(z)+ exp((c - 1)* Pi*I)*(GAMMA(c - 1)*GAMMA(b - a + 1))/(GAMMA(b)*GAMMA(c - a))*w[2]*(z) Subscript[w, 6]*(z)=Divide[Gamma[1 - c]*Gamma[b - a + 1],Gamma[b - c + 1]*Gamma[1 - a]]*Subscript[w, 1]*(z)+ Exp[(c - 1)* Pi*I]*Divide[Gamma[c - 1]*Gamma[b - a + 1],Gamma[b]*Gamma[c - a]]*Subscript[w, 2]*(z) Failure Failure Skip Error
15.10.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = \frac{\EulerGamma@{c}\EulerGamma@{c-a-b}}{\EulerGamma@{c-a}\EulerGamma@{c-b}}w_{3}(z)+\frac{\EulerGamma@{c}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{b}}w_{4}(z)} w[1]*(z)=(GAMMA(c)*GAMMA(c - a - b))/(GAMMA(c - a)*GAMMA(c - b))*w[3]*(z)+(GAMMA(c)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(b))*w[4]*(z) Subscript[w, 1]*(z)=Divide[Gamma[c]*Gamma[c - a - b],Gamma[c - a]*Gamma[c - b]]*Subscript[w, 3]*(z)+Divide[Gamma[c]*Gamma[a + b - c],Gamma[a]*Gamma[b]]*Subscript[w, 4]*(z) Failure Failure Skip Error
15.10.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = \frac{\EulerGamma@{2-c}\EulerGamma@{c-a-b}}{\EulerGamma@{1-a}\EulerGamma@{1-b}}w_{3}(z)+\frac{\EulerGamma@{2-c}\EulerGamma@{a+b-c}}{\EulerGamma@{a-c+1}\EulerGamma@{b-c+1}}w_{4}(z)} w[2]*(z)=(GAMMA(2 - c)*GAMMA(c - a - b))/(GAMMA(1 - a)*GAMMA(1 - b))*w[3]*(z)+(GAMMA(2 - c)*GAMMA(a + b - c))/(GAMMA(a - c + 1)*GAMMA(b - c + 1))*w[4]*(z) Subscript[w, 2]*(z)=Divide[Gamma[2 - c]*Gamma[c - a - b],Gamma[1 - a]*Gamma[1 - b]]*Subscript[w, 3]*(z)+Divide[Gamma[2 - c]*Gamma[a + b - c],Gamma[a - c + 1]*Gamma[b - c + 1]]*Subscript[w, 4]*(z) Failure Failure Skip Error
15.10.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{5}(z) = e^{a\pi\iunit}\frac{\EulerGamma@{a-b+1}\EulerGamma@{c-a-b}}{\EulerGamma@{1-b}\EulerGamma@{c-b}}w_{3}(z)+e^{(c-b)\pi\iunit}\frac{\EulerGamma@{a-b+1}\EulerGamma@{a+b-c}}{\EulerGamma@{a}\EulerGamma@{a-c+1}}w_{4}(z)} w[5]*(z)= exp(a*Pi*I)*(GAMMA(a - b + 1)*GAMMA(c - a - b))/(GAMMA(1 - b)*GAMMA(c - b))*w[3]*(z)+ exp((c - b)* Pi*I)*(GAMMA(a - b + 1)*GAMMA(a + b - c))/(GAMMA(a)*GAMMA(a - c + 1))*w[4]*(z) Subscript[w, 5]*(z)= Exp[a*Pi*I]*Divide[Gamma[a - b + 1]*Gamma[c - a - b],Gamma[1 - b]*Gamma[c - b]]*Subscript[w, 3]*(z)+ Exp[(c - b)* Pi*I]*Divide[Gamma[a - b + 1]*Gamma[a + b - c],Gamma[a]*Gamma[a - c + 1]]*Subscript[w, 4]*(z) Failure Failure Skip Error
15.10.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{6}(z) = e^{b\pi\iunit}\frac{\EulerGamma@{b-a+1}\EulerGamma@{c-a-b}}{\EulerGamma@{1-a}\EulerGamma@{c-a}}w_{3}(z)+e^{(c-a)\pi\iunit}\frac{\EulerGamma@{b-a+1}\EulerGamma@{a+b-c}}{\EulerGamma@{b}\EulerGamma@{b-c+1}}w_{4}(z)} w[6]*(z)= exp(b*Pi*I)*(GAMMA(b - a + 1)*GAMMA(c - a - b))/(GAMMA(1 - a)*GAMMA(c - a))*w[3]*(z)+ exp((c - a)* Pi*I)*(GAMMA(b - a + 1)*GAMMA(a + b - c))/(GAMMA(b)*GAMMA(b - c + 1))*w[4]*(z) Subscript[w, 6]*(z)= Exp[b*Pi*I]*Divide[Gamma[b - a + 1]*Gamma[c - a - b],Gamma[1 - a]*Gamma[c - a]]*Subscript[w, 3]*(z)+ Exp[(c - a)* Pi*I]*Divide[Gamma[b - a + 1]*Gamma[a + b - c],Gamma[b]*Gamma[b - c + 1]]*Subscript[w, 4]*(z) Failure Failure Skip Error
15.10.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = \frac{\EulerGamma@{c}\EulerGamma@{b-a}}{\EulerGamma@{b}\EulerGamma@{c-a}}w_{5}(z)+\frac{\EulerGamma@{c}\EulerGamma@{a-b}}{\EulerGamma@{a}\EulerGamma@{c-b}}w_{6}(z)} w[1]*(z)=(GAMMA(c)*GAMMA(b - a))/(GAMMA(b)*GAMMA(c - a))*w[5]*(z)+(GAMMA(c)*GAMMA(a - b))/(GAMMA(a)*GAMMA(c - b))*w[6]*(z) Subscript[w, 1]*(z)=Divide[Gamma[c]*Gamma[b - a],Gamma[b]*Gamma[c - a]]*Subscript[w, 5]*(z)+Divide[Gamma[c]*Gamma[a - b],Gamma[a]*Gamma[c - b]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = e^{(1-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b-a}}{\EulerGamma@{1-a}\EulerGamma@{b-c+1}}w_{5}(z)+e^{(1-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a-b}}{\EulerGamma@{1-b}\EulerGamma@{a-c+1}}w_{6}(z)} w[2]*(z)= exp((1 - c)* Pi*I)*(GAMMA(2 - c)*GAMMA(b - a))/(GAMMA(1 - a)*GAMMA(b - c + 1))*w[5]*(z)+ exp((1 - c)* Pi*I)*(GAMMA(2 - c)*GAMMA(a - b))/(GAMMA(1 - b)*GAMMA(a - c + 1))*w[6]*(z) Subscript[w, 2]*(z)= Exp[(1 - c)* Pi*I]*Divide[Gamma[2 - c]*Gamma[b - a],Gamma[1 - a]*Gamma[b - c + 1]]*Subscript[w, 5]*(z)+ Exp[(1 - c)* Pi*I]*Divide[Gamma[2 - c]*Gamma[a - b],Gamma[1 - b]*Gamma[a - c + 1]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{3}(z) = e^{-a\pi\iunit}\frac{\EulerGamma@{a+b-c+1}\EulerGamma@{b-a}}{\EulerGamma@{b}\EulerGamma@{b-c+1}}w_{5}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{a+b-c+1}\EulerGamma@{a-b}}{\EulerGamma@{a}\EulerGamma@{a-c+1}}w_{6}(z)} w[3]*(z)= exp(- a*Pi*I)*(GAMMA(a + b - c + 1)*GAMMA(b - a))/(GAMMA(b)*GAMMA(b - c + 1))*w[5]*(z)+ exp(- b*Pi*I)*(GAMMA(a + b - c + 1)*GAMMA(a - b))/(GAMMA(a)*GAMMA(a - c + 1))*w[6]*(z) Subscript[w, 3]*(z)= Exp[- a*Pi*I]*Divide[Gamma[a + b - c + 1]*Gamma[b - a],Gamma[b]*Gamma[b - c + 1]]*Subscript[w, 5]*(z)+ Exp[- b*Pi*I]*Divide[Gamma[a + b - c + 1]*Gamma[a - b],Gamma[a]*Gamma[a - c + 1]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{4}(z) = e^{(b-c)\pi\iunit}\frac{\EulerGamma@{c-a-b+1}\EulerGamma@{b-a}}{\EulerGamma@{1-a}\EulerGamma@{c-a}}w_{5}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{c-a-b+1}\EulerGamma@{a-b}}{\EulerGamma@{1-b}\EulerGamma@{c-b}}w_{6}(z)} w[4]*(z)= exp((b - c)* Pi*I)*(GAMMA(c - a - b + 1)*GAMMA(b - a))/(GAMMA(1 - a)*GAMMA(c - a))*w[5]*(z)+ exp((a - c)* Pi*I)*(GAMMA(c - a - b + 1)*GAMMA(a - b))/(GAMMA(1 - b)*GAMMA(c - b))*w[6]*(z) Subscript[w, 4]*(z)= Exp[(b - c)* Pi*I]*Divide[Gamma[c - a - b + 1]*Gamma[b - a],Gamma[1 - a]*Gamma[c - a]]*Subscript[w, 5]*(z)+ Exp[(a - c)* Pi*I]*Divide[Gamma[c - a - b + 1]*Gamma[a - b],Gamma[1 - b]*Gamma[c - b]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = e^{b\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{a-c+1}}{\EulerGamma@{a+b-c+1}\EulerGamma@{c-b}}w_{3}(z)+e^{(b-c)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{a-c+1}}{\EulerGamma@{b}\EulerGamma@{a-b+1}}w_{5}(z)} w[1]*(z)= exp(b*Pi*I)*(GAMMA(c)*GAMMA(a - c + 1))/(GAMMA(a + b - c + 1)*GAMMA(c - b))*w[3]*(z)+ exp((b - c)* Pi*I)*(GAMMA(c)*GAMMA(a - c + 1))/(GAMMA(b)*GAMMA(a - b + 1))*w[5]*(z) Subscript[w, 1]*(z)= Exp[b*Pi*I]*Divide[Gamma[c]*Gamma[a - c + 1],Gamma[a + b - c + 1]*Gamma[c - b]]*Subscript[w, 3]*(z)+ Exp[(b - c)* Pi*I]*Divide[Gamma[c]*Gamma[a - c + 1],Gamma[b]*Gamma[a - b + 1]]*Subscript[w, 5]*(z) Failure Failure Skip Error
15.10.E30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = e^{a\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{b-c+1}}{\EulerGamma@{a+b-c+1}\EulerGamma@{c-a}}w_{3}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{b-c+1}}{\EulerGamma@{a}\EulerGamma@{b-a+1}}w_{6}(z)} w[1]*(z)= exp(a*Pi*I)*(GAMMA(c)*GAMMA(b - c + 1))/(GAMMA(a + b - c + 1)*GAMMA(c - a))*w[3]*(z)+ exp((a - c)* Pi*I)*(GAMMA(c)*GAMMA(b - c + 1))/(GAMMA(a)*GAMMA(b - a + 1))*w[6]*(z) Subscript[w, 1]*(z)= Exp[a*Pi*I]*Divide[Gamma[c]*Gamma[b - c + 1],Gamma[a + b - c + 1]*Gamma[c - a]]*Subscript[w, 3]*(z)+ Exp[(a - c)* Pi*I]*Divide[Gamma[c]*Gamma[b - c + 1],Gamma[a]*Gamma[b - a + 1]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = e^{(b-c+1)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a}}{\EulerGamma@{a+b-c+1}\EulerGamma@{1-b}}w_{3}(z)+e^{(b-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{a}}{\EulerGamma@{a-b+1}\EulerGamma@{b-c+1}}w_{5}(z)} w[2]*(z)= exp((b - c + 1)* Pi*I)*(GAMMA(2 - c)*GAMMA(a))/(GAMMA(a + b - c + 1)*GAMMA(1 - b))*w[3]*(z)+ exp((b - c)* Pi*I)*(GAMMA(2 - c)*GAMMA(a))/(GAMMA(a - b + 1)*GAMMA(b - c + 1))*w[5]*(z) Subscript[w, 2]*(z)= Exp[(b - c + 1)* Pi*I]*Divide[Gamma[2 - c]*Gamma[a],Gamma[a + b - c + 1]*Gamma[1 - b]]*Subscript[w, 3]*(z)+ Exp[(b - c)* Pi*I]*Divide[Gamma[2 - c]*Gamma[a],Gamma[a - b + 1]*Gamma[b - c + 1]]*Subscript[w, 5]*(z) Failure Failure Skip Error
15.10.E32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = e^{(a-c+1)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b}}{\EulerGamma@{a+b-c+1}\EulerGamma@{1-a}}w_{3}(z)+e^{(a-c)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{b}}{\EulerGamma@{b-a+1}\EulerGamma@{a-c+1}}w_{6}(z)} w[2]*(z)= exp((a - c + 1)* Pi*I)*(GAMMA(2 - c)*GAMMA(b))/(GAMMA(a + b - c + 1)*GAMMA(1 - a))*w[3]*(z)+ exp((a - c)* Pi*I)*(GAMMA(2 - c)*GAMMA(b))/(GAMMA(b - a + 1)*GAMMA(a - c + 1))*w[6]*(z) Subscript[w, 2]*(z)= Exp[(a - c + 1)* Pi*I]*Divide[Gamma[2 - c]*Gamma[b],Gamma[a + b - c + 1]*Gamma[1 - a]]*Subscript[w, 3]*(z)+ Exp[(a - c)* Pi*I]*Divide[Gamma[2 - c]*Gamma[b],Gamma[b - a + 1]*Gamma[a - c + 1]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = e^{(c-a)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-b}}{\EulerGamma@{a}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-a\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-b}}{\EulerGamma@{a-b+1}\EulerGamma@{c-a}}w_{5}(z)} w[1]*(z)= exp((c - a)* Pi*I)*(GAMMA(c)*GAMMA(1 - b))/(GAMMA(a)*GAMMA(c - a - b + 1))*w[4]*(z)+ exp(- a*Pi*I)*(GAMMA(c)*GAMMA(1 - b))/(GAMMA(a - b + 1)*GAMMA(c - a))*w[5]*(z) Subscript[w, 1]*(z)= Exp[(c - a)* Pi*I]*Divide[Gamma[c]*Gamma[1 - b],Gamma[a]*Gamma[c - a - b + 1]]*Subscript[w, 4]*(z)+ Exp[- a*Pi*I]*Divide[Gamma[c]*Gamma[1 - b],Gamma[a - b + 1]*Gamma[c - a]]*Subscript[w, 5]*(z) Failure Failure Skip Error
15.10.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(z) = e^{(c-b)\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-a}}{\EulerGamma@{b}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{c}\EulerGamma@{1-a}}{\EulerGamma@{b-a+1}\EulerGamma@{c-b}}w_{6}(z)} w[1]*(z)= exp((c - b)* Pi*I)*(GAMMA(c)*GAMMA(1 - a))/(GAMMA(b)*GAMMA(c - a - b + 1))*w[4]*(z)+ exp(- b*Pi*I)*(GAMMA(c)*GAMMA(1 - a))/(GAMMA(b - a + 1)*GAMMA(c - b))*w[6]*(z) Subscript[w, 1]*(z)= Exp[(c - b)* Pi*I]*Divide[Gamma[c]*Gamma[1 - a],Gamma[b]*Gamma[c - a - b + 1]]*Subscript[w, 4]*(z)+ Exp[- b*Pi*I]*Divide[Gamma[c]*Gamma[1 - a],Gamma[b - a + 1]*Gamma[c - b]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.10.E35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = e^{(1-a)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-b}}{\EulerGamma@{a-c+1}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-a\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-b}}{\EulerGamma@{a-b+1}\EulerGamma@{1-a}}w_{5}(z)} w[2]*(z)= exp((1 - a)* Pi*I)*(GAMMA(2 - c)*GAMMA(c - b))/(GAMMA(a - c + 1)*GAMMA(c - a - b + 1))*w[4]*(z)+ exp(- a*Pi*I)*(GAMMA(2 - c)*GAMMA(c - b))/(GAMMA(a - b + 1)*GAMMA(1 - a))*w[5]*(z) Subscript[w, 2]*(z)= Exp[(1 - a)* Pi*I]*Divide[Gamma[2 - c]*Gamma[c - b],Gamma[a - c + 1]*Gamma[c - a - b + 1]]*Subscript[w, 4]*(z)+ Exp[- a*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - b],Gamma[a - b + 1]*Gamma[1 - a]]*Subscript[w, 5]*(z) Failure Failure Skip Error
15.10.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z) = e^{(1-b)\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-a}}{\EulerGamma@{b-c+1}\EulerGamma@{c-a-b+1}}w_{4}(z)+e^{-b\pi\iunit}\frac{\EulerGamma@{2-c}\EulerGamma@{c-a}}{\EulerGamma@{b-a+1}\EulerGamma@{1-b}}w_{6}(z)} w[2]*(z)= exp((1 - b)* Pi*I)*(GAMMA(2 - c)*GAMMA(c - a))/(GAMMA(b - c + 1)*GAMMA(c - a - b + 1))*w[4]*(z)+ exp(- b*Pi*I)*(GAMMA(2 - c)*GAMMA(c - a))/(GAMMA(b - a + 1)*GAMMA(1 - b))*w[6]*(z) Subscript[w, 2]*(z)= Exp[(1 - b)* Pi*I]*Divide[Gamma[2 - c]*Gamma[c - a],Gamma[b - c + 1]*Gamma[c - a - b + 1]]*Subscript[w, 4]*(z)+ Exp[- b*Pi*I]*Divide[Gamma[2 - c]*Gamma[c - a],Gamma[b - a + 1]*Gamma[1 - b]]*Subscript[w, 6]*(z) Failure Failure Skip Error
15.12.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{+} = \atan@{\frac{\phase@@{z}-\phase@{1-z}-\pi}{\ln@@{|1-z^{-1}|}}}} alpha[+]= arctan((argument(z)- argument(1 - z)- Pi)/(ln(abs(1 - (z)^(- 1))))) Subscript[\[Alpha], +]= ArcTan[Divide[Arg[z]- Arg[1 - z]- Pi,Log[Abs[1 - (z)^(- 1)]]]] Error Failure - Error
15.12.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{-} = \atan@{\frac{\phase@@{z}-\phase@{1-z}+\pi}{\ln@@{|1-z^{-1}|}}}} alpha[-]= arctan((argument(z)- argument(1 - z)+ Pi)/(ln(abs(1 - (z)^(- 1))))) Subscript[\[Alpha], -]= ArcTan[Divide[Arg[z]- Arg[1 - z]+ Pi,Log[Abs[1 - (z)^(- 1)]]]] Error Failure - Error
15.12.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \acosh@@{z}} zeta = arccosh(z) \[zeta]= ArcCosh[z] Failure Failure
Fail
.22188930e-1+.5671060437*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
.22188930e-1-2.261321080*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
-2.806238194-2.261321080*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
-2.806238194+.5671060437*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 Error
15.12.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = \left(-2\ln@{1-\left(\frac{z-1}{z+1}\right)^{2}}\right)^{1/2}} alpha =(- 2*ln(1 -((z - 1)/(z + 1))^(2)))^(1/ 2) \[Alpha]=(- 2*Log[1 -(Divide[z - 1,z + 1])^(2)])^(1/ 2) Failure Failure
Fail
.9106437259+.8692893105*I <- {alpha = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
.9106437259+1.959137814*I <- {alpha = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.6547904750+3.198787193*I <- {alpha = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.6547904750-.370360069*I <- {alpha = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 Error
15.12.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \acosh@{\tfrac{1}{4}z-1}} zeta = arccosh((1)/(4)*z - 1) \[zeta]= ArcCosh[Divide[1,4]*z - 1] Failure Failure
Fail
.9885072570-.790108118*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
.9885072570-3.618535242*I <- {z = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
-1.839919867-3.618535242*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
-1.839919867-.790108118*I <- {z = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 Error
15.12.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \left(-\frac{3}{2}\zeta+\frac{9}{4}\ln@{\frac{2+e^{\zeta}}{2+e^{-\zeta}}}\right)^{1/3}} beta =(-(3)/(2)*zeta +(9)/(4)*ln((2 + exp(zeta))/(2 + exp(- zeta))))^(1/ 3) \[Beta]=(-Divide[3,2]*\[zeta]+Divide[9,4]*Log[Divide[2 + Exp[\[zeta]],2 + Exp[- \[zeta]]]])^(1/ 3) Failure Failure
Fail
.8286036743+.9438951834*I <- {beta = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
.8286036743+1.884531941*I <- {beta = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
.7141009552+1.686207411*I <- {beta = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
.7141009552+1.142219713*I <- {beta = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 Error
15.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle N(a,b,c) = \begin{cases}0,&a} N*(a , b , c)= N*(a , b , c)= Error Failure - Error
15.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{cases}0,&a > 0,\\ \floor{-a}+\tfrac{1}{2}(1+S),&a} Error Failure - Error
15.13.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0,\\ \floor{-a}+\tfrac{1}{2}(1+S),&a < 0,c-a} 0 , floor(- a)+(1)/(2)*(1 + S), 0 , Floor[- a]+Divide[1,2]*(1 + S), Error Failure - Error
15.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{s-1}\hyperOlverF@@{a}{b}{c}{-x}\diff{x} = \frac{\EulerGamma@{s}\EulerGamma@{a-s}\EulerGamma@{b-s}}{\EulerGamma@{a}\EulerGamma@{b}\EulerGamma@{c-s}}} int((x)^(s - 1)* hypergeom([a, b], [c], - x)/GAMMA(c), x = 0..infinity)=(GAMMA(s)*GAMMA(a - s)*GAMMA(b - s))/(GAMMA(a)*GAMMA(b)*GAMMA(c - s)) Integrate[(x)^(s - 1)* Hypergeometric2F1Regularized[a, b, c, - x], {x, 0, Infinity}]=Divide[Gamma[s]*Gamma[a - s]*Gamma[b - s],Gamma[a]*Gamma[b]*Gamma[c - s]] Successful Failure - Error
15.15.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@@{a}{b}{c}{\frac{1}{z}} = \left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*\hyperOlverF@@{-s}{b}{c}{\frac{1}{z_{0}}}\left(1-\frac{z}{z_{0}}\right)^{-s}} hypergeom([a, b], [c], (1)/(z))/GAMMA(c)=(1 -(z[0])/(z))^(- a)* sum((a[s])/(factorial(s))* hypergeom([- s, b], [c], (1)/(z[0]))/GAMMA(c)*(1 -(z)/(z[0]))^(- s), s = 0..infinity) Hypergeometric2F1Regularized[a, b, c, Divide[1,z]]=(1 -Divide[Subscript[z, 0],z])^(- a)* Sum[Divide[Subscript[a, s],(s)!]* Hypergeometric2F1Regularized[- s, b, c, Divide[1,Subscript[z, 0]]]*(1 -Divide[z,Subscript[z, 0]])^(- s), {s, 0, Infinity}] Failure Failure Skip Error
15.16.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{c-\frac{1}{2}}{z}\hyperF@@{c-a}{c-b}{c+\frac{1}{2}}{z} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{c}{s}}{\Pochhammersym{c+\frac{1}{2}}{s}}A_{s}z^{s}} hypergeom([a, b], [c -(1)/(2)], z)*hypergeom([c - a, c - b], [c +(1)/(2)], z)= sum((pochhammer(c, s))/(pochhammer(c +(1)/(2), s))*A[s]*(z)^(s), s = 0..infinity) Hypergeometric2F1[a, b, c -Divide[1,2], z]*Hypergeometric2F1[c - a, c - b, c +Divide[1,2], z]= Sum[Divide[Pochhammer[c, s],Pochhammer[c +Divide[1,2], s]]*Subscript[A, s]*(z)^(s), {s, 0, Infinity}] Failure Failure Skip Error
15.16.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-z)^{a+b-c}\hyperF@{2a}{2b}{2c-1}{z} = \sum_{s=0}^{\infty}A_{s}z^{s}} (1 - z)^(a + b - c)* hypergeom([2*a, 2*b], [2*c - 1], z)= sum(A[s]*(z)^(s), s = 0..infinity) (1 - z)^(a + b - c)* Hypergeometric2F1[2*a, 2*b, 2*c - 1, z]= Sum[Subscript[A, s]*(z)^(s), {s, 0, Infinity}] Failure Failure Skip Error
15.16.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{c}{z}\hyperF@@{a}{b}{c}{\zeta} = \sum_{s=0}^{\infty}\frac{\Pochhammersym{a}{s}\Pochhammersym{b}{s}\Pochhammersym{c-a}{s}\Pochhammersym{c-b}{s}}{\Pochhammersym{c}{s}\Pochhammersym{c}{2s}s!}\left(z\zeta\right)^{s}\hyperF@@{a+s}{b+s}{c+2s}{z+\zeta-z\zeta}} hypergeom([a, b], [c], z)*hypergeom([a, b], [c], zeta)= sum((pochhammer(a, s)*pochhammer(b, s)*pochhammer(c - a, s)*pochhammer(c - b, s))/(pochhammer(c, s)*pochhammer(c, 2*s)*factorial(s))*(z*zeta)^(s)* hypergeom([a + s, b + s], [c + 2*s], z + zeta - z*zeta), s = 0..infinity) Hypergeometric2F1[a, b, c, z]*Hypergeometric2F1[a, b, c, \[zeta]]= Sum[Divide[Pochhammer[a, s]*Pochhammer[b, s]*Pochhammer[c - a, s]*Pochhammer[c - b, s],Pochhammer[c, s]*Pochhammer[c, 2*s]*(s)!]*(z*\[zeta])^(s)* Hypergeometric2F1[a + s, b + s, c + 2*s, z + \[zeta]- z*\[zeta]], {s, 0, Infinity}] Failure Failure Skip Error
15.16.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{a}{b}{c}{z}\hyperF@@{-a}{-b}{-c}{z}+\frac{ab(a-c)(b-c)}{c^{2}(1-c^{2})}z^{2}\hyperF@@{1+a}{1+b}{2+c}{z}\hyperF@@{1-a}{1-b}{2-c}{z} = 1} hypergeom([a, b], [c], z)*hypergeom([- a, - b], [- c], z)+(a*b*(a - c)*(b - c))/((c)^(2)*(1 - (c)^(2)))*(z)^(2)* hypergeom([1 + a, 1 + b], [2 + c], z)*hypergeom([1 - a, 1 - b], [2 - c], z)= 1 Hypergeometric2F1[a, b, c, z]*Hypergeometric2F1[- a, - b, - c, z]+Divide[a*b*(a - c)*(b - c),(c)^(2)*(1 - (c)^(2))]*(z)^(2)* Hypergeometric2F1[1 + a, 1 + b, 2 + c, z]*Hypergeometric2F1[1 - a, 1 - b, 2 - c, z]= 1 Failure Failure Successful Error
15.16.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{\frac{1}{2}+\lambda}{-\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z}+\hyperF@@{\frac{1}{2}+\lambda}{\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{-\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z}-\hyperF@@{\frac{1}{2}+\lambda}{\frac{1}{2}-\nu}{1+\lambda+\mu}{z}\hyperF@@{\frac{1}{2}-\lambda}{\frac{1}{2}+\nu}{1+\nu+\mu}{1-z} = \frac{\EulerGamma@{1+\lambda+\mu}\EulerGamma@{1+\nu+\mu}}{\EulerGamma@{\lambda+\mu+\nu+\frac{3}{2}}\EulerGamma@{\frac{1}{2}+\nu}}} hypergeom([(1)/(2)+ lambda, -(1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z)+ hypergeom([(1)/(2)+ lambda, (1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([-(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z)- hypergeom([(1)/(2)+ lambda, (1)/(2)- nu], [1 + lambda + mu], z)*hypergeom([(1)/(2)- lambda, (1)/(2)+ nu], [1 + nu + mu], 1 - z)=(GAMMA(1 + lambda + mu)*GAMMA(1 + nu + mu))/(GAMMA(lambda + mu + nu +(3)/(2))*GAMMA((1)/(2)+ nu)) Hypergeometric2F1[Divide[1,2]+ \[Lambda], -Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z]+ Hypergeometric2F1[Divide[1,2]+ \[Lambda], Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[-Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z]- Hypergeometric2F1[Divide[1,2]+ \[Lambda], Divide[1,2]- \[Nu], 1 + \[Lambda]+ \[Mu], z]*Hypergeometric2F1[Divide[1,2]- \[Lambda], Divide[1,2]+ \[Nu], 1 + \[Nu]+ \[Mu], 1 - z]=Divide[Gamma[1 + \[Lambda]+ \[Mu]]*Gamma[1 + \[Nu]+ \[Mu]],Gamma[\[Lambda]+ \[Mu]+ \[Nu]+Divide[3,2]]*Gamma[Divide[1,2]+ \[Nu]]] Failure Failure Skip Error
Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Results_of_Hypergeometric_Function&oldid=63464"