Results of Parabolic Cylinder Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 12.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}-\left(\tfrac{1}{4}z^{2}+a\right)w = 0} | diff(w, [z$(2)])-((1)/(4)*(z)^(2)+ a)* w = 0 |
D[w, {z, 2}]-(Divide[1,4]*(z)^(2)+ a)* w = 0 |
Failure | Failure | Fail 1.414213562-5.414213560*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.414213561-2.585786437*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.414213561-2.585786437*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[1.4142135623730945, -5.414213562373096] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730954, -2.5857864376269055] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730945, -5.414213562373096] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730954, -2.5857864376269055] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(\tfrac{1}{4}z^{2}-a\right)w = 0} | diff(w, [z$(2)])+((1)/(4)*(z)^(2)- a)* w = 0 |
D[w, {z, 2}]+(Divide[1,4]*(z)^(2)- a)* w = 0 |
Failure | Failure | Fail -1.414213561-2.585786437*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}1.414213562-5.414213560*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}-1.414213561-2.585786437*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.414213562-5.414213560*I <- {a = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-1.4142135623730954, -2.5857864376269055] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730945, -5.414213562373096] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730954, -2.5857864376269055] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730945, -5.414213562373096] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, 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 |
| 12.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(\nu+\tfrac{1}{2}-\tfrac{1}{4}z^{2}\right)w = 0} | diff(w, [z$(2)])+(nu +(1)/(2)-(1)/(4)*(z)^(2))* w = 0 |
D[w, {z, 2}]+(\[Nu]+Divide[1,2]-Divide[1,4]*(z)^(2))* w = 0 |
Failure | Failure | Fail 2.121320342+3.292893218*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-.7071067810+6.121320341*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}2.121320342+3.292893218*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.7071067810+6.121320341*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[2.121320343559643, 3.292893218813453] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[6.121320343559643, -0.707106781186547] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.121320343559642, -4.707106781186548] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.8786796564403578, -0.7071067811865477] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerparaD{\nu}@{z} = \paraU@{-\tfrac{1}{2}-\nu}{z}} | CylinderD(nu, z)= CylinderU(-(1)/(2)- nu, z) |
ParabolicCylinderD[\[Nu], z]= ParabolicCylinderD[--Divide[1,2]- \[Nu] - 1/2, z] |
Successful | Failure | - | Fail
Complex[0.6373277951223405, 0.24855575768220314] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[5.494742013097394, -8.693674717807955] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.2264312008959464, -0.021546439055701437] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.3291655729814447, 3.7734764780430785] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ν, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{0} = \frac{\sqrt{\pi}}{2^{\frac{1}{2}a+\frac{1}{4}}\EulerGamma@{\frac{3}{4}+\frac{1}{2}a}}} | CylinderU(a, 0)=(sqrt(Pi))/((2)^((1)/(2)*a +(1)/(4))* GAMMA((3)/(4)+(1)/(2)*a)) |
ParabolicCylinderD[-a - 1/2, 0]=Divide[Sqrt[Pi],(2)^(Divide[1,2]*a +Divide[1,4])* Gamma[Divide[3,4]+Divide[1,2]*a]] |
Successful | Successful | - | - |
| 12.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU'@{a}{0} = -\frac{\sqrt{\pi}}{2^{\frac{1}{2}a-\frac{1}{4}}\EulerGamma@{\frac{1}{4}+\frac{1}{2}a}}} | subs( temp=0, diff( CylinderU(a, temp), temp$(1) ) )= -(sqrt(Pi))/((2)^((1)/(2)*a -(1)/(4))* GAMMA((1)/(4)+(1)/(2)*a)) |
(D[ParabolicCylinderD[-a - 1/2, temp], {temp, 1}]/.temp-> 0)= -Divide[Sqrt[Pi],(2)^(Divide[1,2]*a -Divide[1,4])* Gamma[Divide[1,4]+Divide[1,2]*a]] |
Successful | Successful | - | - |
| 12.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{0} = \frac{\pi 2^{\frac{1}{2}a+\frac{1}{4}}}{\left(\EulerGamma@{\frac{3}{4}-\frac{1}{2}a}\right)^{2}\EulerGamma@{\frac{1}{4}+\frac{1}{2}a}}} | CylinderV(a, 0)=(Pi*(2)^((1)/(2)*a +(1)/(4)))/((GAMMA((3)/(4)-(1)/(2)*a))^(2)* GAMMA((1)/(4)+(1)/(2)*a)) |
Error |
Successful | Error | - | - |
| 12.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV'@{a}{0} = \frac{\pi 2^{\frac{1}{2}a+\frac{3}{4}}}{\left(\EulerGamma@{\frac{1}{4}-\frac{1}{2}a}\right)^{2}\EulerGamma@{\frac{3}{4}+\frac{1}{2}a}}} | subs( temp=0, diff( CylinderV(a, temp), temp$(1) ) )=(Pi*(2)^((1)/(2)*a +(3)/(4)))/((GAMMA((1)/(4)-(1)/(2)*a))^(2)* GAMMA((3)/(4)+(1)/(2)*a)) |
Error |
Successful | Error | - | - |
| 12.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian\left\{\paraU@{a}{z},\paraV@{a}{z}\right\} = \sqrt{2/\pi}} | (CylinderU(a, z))*diff(CylinderV(a, z), z)-diff(CylinderU(a, z), z)*(CylinderV(a, z))=sqrt(2/ Pi) |
Error |
Failure | Error | Successful | - |
| 12.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian\left\{\paraU@{a}{z},\paraU@{a}{-z}\right\} = \frac{\sqrt{2\pi}}{\EulerGamma@{\frac{1}{2}+a}}} | (CylinderU(a, z))*diff(CylinderU(a, - z), z)-diff(CylinderU(a, z), z)*(CylinderU(a, - z))=(sqrt(2*Pi))/(GAMMA((1)/(2)+ a)) |
Wronskian[{ParabolicCylinderD[-a - 1/2, z], ParabolicCylinderD[-a - 1/2, - z]}, z]=Divide[Sqrt[2*Pi],Gamma[Divide[1,2]+ a]] |
Failure | Failure | Successful | Successful |
| 12.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian\left\{\paraU@{a}{z},\paraU@{-a}{+ iz}\right\} = - ie^{+ i\pi(\frac{1}{2}a+\frac{1}{4})}} | (CylinderU(a, z))*diff(CylinderU(- a, + I*z), z)-diff(CylinderU(a, z), z)*(CylinderU(- a, + I*z))= - I*exp(+ I*Pi*((1)/(2)*a +(1)/(4))) |
Wronskian[{ParabolicCylinderD[-a - 1/2, z], ParabolicCylinderD[-- a - 1/2, + I*z]}, z]= - I*Exp[+ I*Pi*(Divide[1,2]*a +Divide[1,4])] |
Failure | Failure | Successful | Fail
Complex[0.14811550020669734, -0.23555829917293641] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.05275467566832733, -0.08637346425615816] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.393334833694336, -1.5801979189958324] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-124.21447949802922, -41.9141177725009] <- {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 |
| 12.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian\left\{\paraU@{a}{z},\paraU@{-a}{- iz}\right\} = + ie^{- i\pi(\frac{1}{2}a+\frac{1}{4})}} | (CylinderU(a, z))*diff(CylinderU(- a, - I*z), z)-diff(CylinderU(a, z), z)*(CylinderU(- a, - I*z))= + I*exp(- I*Pi*((1)/(2)*a +(1)/(4))) |
Wronskian[{ParabolicCylinderD[-a - 1/2, z], ParabolicCylinderD[-- a - 1/2, - I*z]}, z]= + I*Exp[- I*Pi*(Divide[1,2]*a +Divide[1,4])] |
Failure | Failure | Successful | Fail
Complex[1.7828893409022697, 7.309124598403374] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[3.6470896010983296, 11.133201917893151] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[12.667352367459173, 6.462811262967247] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[1.2682027250441195, 0.1306629371451986] <- {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 |
| 12.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{-n-\tfrac{1}{2}}{-z} = (-1)^{n}\paraU@{-n-\tfrac{1}{2}}{z}} | CylinderU(- n -(1)/(2), - z)=(- 1)^(n)* CylinderU(- n -(1)/(2), z) |
ParabolicCylinderD[-- n -Divide[1,2] - 1/2, - z]=(- 1)^(n)* ParabolicCylinderD[-- n -Divide[1,2] - 1/2, z] |
Failure | Failure | Successful | Successful |
| 12.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{n+\tfrac{1}{2}}{-z} = (-1)^{n}\paraV@{n+\tfrac{1}{2}}{z}} | CylinderV(n +(1)/(2), - z)=(- 1)^(n)* CylinderV(n +(1)/(2), z) |
Error |
Failure | Error | Successful | - |
| 12.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{-z} = -\sin@{\pi a}\paraU@{a}{z}+\frac{\pi}{\EulerGamma@{\frac{1}{2}+a}}\paraV@{a}{z}} | CylinderU(a, - z)= - sin(Pi*a)*CylinderU(a, z)+(Pi)/(GAMMA((1)/(2)+ a))*CylinderV(a, z) |
Error |
Successful | Error | - | - |
| 12.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{-z} = \frac{\cos@{\pi a}}{\EulerGamma@{\frac{1}{2}-a}}\paraU@{a}{z}+\sin@{\pi a}\paraV@{a}{z}} | CylinderV(a, - z)=(cos(Pi*a))/(GAMMA((1)/(2)- a))*CylinderU(a, z)+ sin(Pi*a)*CylinderV(a, z) |
Error |
Failure | Error | Successful | - |
| 12.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2\pi}\paraU@{-a}{+ iz} = \EulerGamma@{\tfrac{1}{2}+a}\left(e^{- i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{a}{z}+e^{+ i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{a}{-z}\right)} | sqrt(2*Pi)*CylinderU(- a, + I*z)= GAMMA((1)/(2)+ a)*(exp(- I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(a, z)+ exp(+ I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(a, - z)) |
Sqrt[2*Pi]*ParabolicCylinderD[-- a - 1/2, + I*z]= Gamma[Divide[1,2]+ a]*(Exp[- I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-a - 1/2, z]+ Exp[+ I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-a - 1/2, - z]) |
Failure | Failure | Successful | Fail
Complex[-2.155433665722218, -2.0290531891335233] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.3367861286344187, -0.6580032872978093] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-5.914157355854969, -11.153359556689384] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[92.56613149692683, 18.07525013091991] <- {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 |
| 12.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2\pi}\paraU@{-a}{- iz} = \EulerGamma@{\tfrac{1}{2}+a}\left(e^{+ i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{a}{z}+e^{- i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{a}{-z}\right)} | sqrt(2*Pi)*CylinderU(- a, - I*z)= GAMMA((1)/(2)+ a)*(exp(+ I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(a, z)+ exp(- I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(a, - z)) |
Sqrt[2*Pi]*ParabolicCylinderD[-- a - 1/2, - I*z]= Gamma[Divide[1,2]+ a]*(Exp[+ I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-a - 1/2, z]+ Exp[- I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-a - 1/2, - z]) |
Failure | Failure | Successful | Fail
Complex[-5.914157355854969, -11.153359556689384] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[92.56613149692683, 18.07525013091991] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.155433665722218, -2.0290531891335233] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.3367861286344187, -0.6580032872978093] <- {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 |
| 12.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2\pi}\paraU@{a}{z} = \EulerGamma@{\tfrac{1}{2}-a}\left(e^{- i\pi(\frac{1}{2}a+\frac{1}{4})}\paraU@{-a}{+ iz}+e^{+ i\pi(\frac{1}{2}a+\frac{1}{4})}\paraU@{-a}{- iz}\right)} | sqrt(2*Pi)*CylinderU(a, z)= GAMMA((1)/(2)- a)*(exp(- I*Pi*((1)/(2)*a +(1)/(4)))*CylinderU(- a, + I*z)+ exp(+ I*Pi*((1)/(2)*a +(1)/(4)))*CylinderU(- a, - I*z)) |
Sqrt[2*Pi]*ParabolicCylinderD[-a - 1/2, z]= Gamma[Divide[1,2]- a]*(Exp[- I*Pi*(Divide[1,2]*a +Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, + I*z]+ Exp[+ I*Pi*(Divide[1,2]*a +Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, - I*z]) |
Failure | Failure | Successful | Fail
Complex[0.10912779491905389, 1.6001420083926765] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5516631154927725, 0.012853611485611899] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6505649452472415, 6.316478461243763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-28.79709943083936, -39.22297340462678] <- {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 |
| 12.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{2\pi}\paraU@{a}{z} = \EulerGamma@{\tfrac{1}{2}-a}\left(e^{+ i\pi(\frac{1}{2}a+\frac{1}{4})}\paraU@{-a}{- iz}+e^{- i\pi(\frac{1}{2}a+\frac{1}{4})}\paraU@{-a}{+ iz}\right)} | sqrt(2*Pi)*CylinderU(a, z)= GAMMA((1)/(2)- a)*(exp(+ I*Pi*((1)/(2)*a +(1)/(4)))*CylinderU(- a, - I*z)+ exp(- I*Pi*((1)/(2)*a +(1)/(4)))*CylinderU(- a, + I*z)) |
Sqrt[2*Pi]*ParabolicCylinderD[-a - 1/2, z]= Gamma[Divide[1,2]- a]*(Exp[+ I*Pi*(Divide[1,2]*a +Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, - I*z]+ Exp[- I*Pi*(Divide[1,2]*a +Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, + I*z]) |
Failure | Failure | Successful | Fail
Complex[0.10912779491905389, 1.6001420083926765] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5516631154927725, 0.012853611485611899] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.6505649452472415, 6.316478461243763] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-28.79709943083936, -39.22297340462678] <- {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 |
| 12.2.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = + ie^{+ i\pi a}\paraU@{a}{-z}+\frac{\sqrt{2\pi}}{\EulerGamma@{\tfrac{1}{2}+a}}e^{+ i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{-a}{+ iz}} | CylinderU(a, z)= + I*exp(+ I*Pi*a)*CylinderU(a, - z)+(sqrt(2*Pi))/(GAMMA((1)/(2)+ a))*exp(+ I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(- a, + I*z) |
ParabolicCylinderD[-a - 1/2, z]= + I*Exp[+ I*Pi*a]*ParabolicCylinderD[-a - 1/2, - z]+Divide[Sqrt[2*Pi],Gamma[Divide[1,2]+ a]]*Exp[+ I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, + I*z] |
Failure | Failure | Successful | Fail
Complex[0.04310956766516494, 0.6077329076178599] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.040829587948855356, 0.14655410699953625] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.6609728840735412, 2.5128092684920165] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-11.485901419364549, -15.648449818478493] <- {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 |
| 12.2.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = - ie^{- i\pi a}\paraU@{a}{-z}+\frac{\sqrt{2\pi}}{\EulerGamma@{\tfrac{1}{2}+a}}e^{- i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{-a}{- iz}} | CylinderU(a, z)= - I*exp(- I*Pi*a)*CylinderU(a, - z)+(sqrt(2*Pi))/(GAMMA((1)/(2)+ a))*exp(- I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(- a, - I*z) |
ParabolicCylinderD[-a - 1/2, z]= - I*Exp[- I*Pi*a]*ParabolicCylinderD[-a - 1/2, - z]+Divide[Sqrt[2*Pi],Gamma[Divide[1,2]+ a]]*Exp[- I*Pi*(Divide[1,2]*a -Divide[1,4])]*ParabolicCylinderD[-- a - 1/2, - I*z] |
Failure | Failure | Successful | Fail
Complex[111.04952307011636, -190.96406860603162] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[587.0445111625338, 1542.4071633053381] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[10.224359018803703, -50.78000597255555] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[6.66355099948441, -11.085954332579782] <- {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 |
| 12.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{z} = \frac{- i}{\EulerGamma@{\frac{1}{2}-a}}\paraU@{a}{z}+\sqrt{\frac{2}{\pi}}e^{- i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{-a}{+ iz}} | CylinderV(a, z)=(- I)/(GAMMA((1)/(2)- a))*CylinderU(a, z)+sqrt((2)/(Pi))*exp(- I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(- a, + I*z) |
Error |
Failure | Error | Successful | - |
| 12.2.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{z} = \frac{+ i}{\EulerGamma@{\frac{1}{2}-a}}\paraU@{a}{z}+\sqrt{\frac{2}{\pi}}e^{+ i\pi(\frac{1}{2}a-\frac{1}{4})}\paraU@{-a}{- iz}} | CylinderV(a, z)=(+ I)/(GAMMA((1)/(2)- a))*CylinderU(a, z)+sqrt((2)/(Pi))*exp(+ I*Pi*((1)/(2)*a -(1)/(4)))*CylinderU(- a, - I*z) |
Error |
Failure | Error | Successful | - |
| 12.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \paraU@{a}{0}u_{1}(a,z)+\paraU'@{a}{0}u_{2}(a,z)} | CylinderU(a, z)= CylinderU(a, 0)*u[1]*(a , z)+ subs( temp=0, diff( CylinderU(a, temp), temp$(1) ) )*u[2]*(a , z) |
ParabolicCylinderD[-a - 1/2, z]= ParabolicCylinderD[-a - 1/2, 0]*Subscript[u, 1]*(a , z)+ (D[ParabolicCylinderD[-a - 1/2, temp], {temp, 1}]/.temp-> 0)*Subscript[u, 2]*(a , z) |
Failure | Failure | Error | Error |
| 12.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{z} = \paraV@{a}{0}u_{1}(a,z)+\paraV'@{a}{0}u_{2}(a,z)} | CylinderV(a, z)= CylinderV(a, 0)*u[1]*(a , z)+ subs( temp=0, diff( CylinderV(a, temp), temp$(1) ) )*u[2]*(a , z) |
Error |
Failure | Error | Error | - |
| 12.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{e^{-\frac{1}{4}z^{2}}}{\EulerGamma@{\frac{1}{2}+a}}\int_{0}^{\infty}t^{a-\frac{1}{2}}e^{-\frac{1}{2}t^{2}-zt}\diff{t}} | CylinderU(a, z)=(exp(-(1)/(4)*(z)^(2)))/(GAMMA((1)/(2)+ a))*int((t)^(a -(1)/(2))* exp(-(1)/(2)*(t)^(2)- z*t), t = 0..infinity) |
ParabolicCylinderD[-a - 1/2, z]=Divide[Exp[-Divide[1,4]*(z)^(2)],Gamma[Divide[1,2]+ a]]*Integrate[(t)^(a -Divide[1,2])* Exp[-Divide[1,2]*(t)^(2)- z*t], {t, 0, Infinity}] |
Successful | Successful | - | - |
| 12.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{ze^{-\frac{1}{4}z^{2}}}{\EulerGamma@{\frac{1}{4}+\frac{1}{2}a}}\*\int_{0}^{\infty}t^{\frac{1}{2}a-\frac{3}{4}}e^{-t}\left(z^{2}+2t\right)^{-\frac{1}{2}a-\frac{3}{4}}\diff{t}} | CylinderU(a, z)=(z*exp(-(1)/(4)*(z)^(2)))/(GAMMA((1)/(4)+(1)/(2)*a))* int((t)^((1)/(2)*a -(3)/(4))* exp(- t)*((z)^(2)+ 2*t)^(-(1)/(2)*a -(3)/(4)), t = 0..infinity) |
ParabolicCylinderD[-a - 1/2, z]=Divide[z*Exp[-Divide[1,4]*(z)^(2)],Gamma[Divide[1,4]+Divide[1,2]*a]]* Integrate[(t)^(Divide[1,2]*a -Divide[3,4])* Exp[- t]*((z)^(2)+ 2*t)^(-Divide[1,2]*a -Divide[3,4]), {t, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 12.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{e^{-\frac{1}{4}z^{2}}}{\EulerGamma@{\frac{3}{4}+\frac{1}{2}a}}\*\int_{0}^{\infty}t^{\frac{1}{2}a-\frac{1}{4}}e^{-t}\left(z^{2}+2t\right)^{-\frac{1}{2}a-\frac{1}{4}}\diff{t}} | CylinderU(a, z)=(exp(-(1)/(4)*(z)^(2)))/(GAMMA((3)/(4)+(1)/(2)*a))* int((t)^((1)/(2)*a -(1)/(4))* exp(- t)*((z)^(2)+ 2*t)^(-(1)/(2)*a -(1)/(4)), t = 0..infinity) |
ParabolicCylinderD[-a - 1/2, z]=Divide[Exp[-Divide[1,4]*(z)^(2)],Gamma[Divide[3,4]+Divide[1,2]*a]]* Integrate[(t)^(Divide[1,2]*a -Divide[1,4])* Exp[- t]*((z)^(2)+ 2*t)^(-Divide[1,2]*a -Divide[1,4]), {t, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 12.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \sqrt{\frac{2}{\pi}}e^{\frac{1}{4}z^{2}}\*\int_{0}^{\infty}t^{-a-\frac{1}{2}}e^{-\frac{1}{2}t^{2}}\cos@{zt+\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)\pi}\diff{t}} | CylinderU(a, z)=sqrt((2)/(Pi))*exp((1)/(4)*(z)^(2))* int((t)^(- a -(1)/(2))* exp(-(1)/(2)*(t)^(2))*cos(z*t +((1)/(2)*a +(1)/(4))* Pi), t = 0..infinity) |
ParabolicCylinderD[-a - 1/2, z]=Sqrt[Divide[2,Pi]]*Exp[Divide[1,4]*(z)^(2)]* Integrate[(t)^(- a -Divide[1,2])* Exp[-Divide[1,2]*(t)^(2)]*Cos[z*t +(Divide[1,2]*a +Divide[1,4])* Pi], {t, 0, Infinity}] |
Successful | Failure | - | Successful |
| 12.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{\EulerGamma@{\frac{1}{2}-a}}{2\pi i}e^{-\frac{1}{4}z^{2}}\int_{-\infty}^{(0+)}e^{zt-\frac{1}{2}t^{2}}t^{a-\frac{1}{2}}\diff{t}} | CylinderU(a, z)=(GAMMA((1)/(2)- a))/(2*Pi*I)*exp(-(1)/(4)*(z)^(2))*int(exp(z*t -(1)/(2)*(t)^(2))*(t)^(a -(1)/(2)), t = - infinity..(0 +)) |
ParabolicCylinderD[-a - 1/2, z]=Divide[Gamma[Divide[1,2]- a],2*Pi*I]*Exp[-Divide[1,4]*(z)^(2)]*Integrate[Exp[z*t -Divide[1,2]*(t)^(2)]*(t)^(a -Divide[1,2]), {t, - Infinity, (0 +)}] |
Error | Failure | - | Error |
| 12.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{e^{\frac{1}{4}z^{2}}}{i\sqrt{2\pi}}\int_{c-i\infty}^{c+i\infty}e^{-zt+\frac{1}{2}t^{2}}t^{-a-\frac{1}{2}}\diff{t}} | CylinderU(a, z)=(exp((1)/(4)*(z)^(2)))/(I*sqrt(2*Pi))*int(exp(- z*t +(1)/(2)*(t)^(2))*(t)^(- a -(1)/(2)), t = c - I*infinity..c + I*infinity) |
ParabolicCylinderD[-a - 1/2, z]=Divide[Exp[Divide[1,4]*(z)^(2)],I*Sqrt[2*Pi]]*Integrate[Exp[- z*t +Divide[1,2]*(t)^(2)]*(t)^(- a -Divide[1,2]), {t, c - I*Infinity, c + I*Infinity}] |
Failure | Failure | Skip | Error |
| 12.5.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = \frac{e^{-\frac{1}{4}z^{2}}z^{-a-\frac{1}{2}}}{2\pi i\EulerGamma@{\frac{1}{2}+a}}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}+a-2t}2^{t}z^{2t}\diff{t}} | CylinderU(a, z)=(exp(-(1)/(4)*(z)^(2))*(z)^(- a -(1)/(2)))/(2*Pi*I*GAMMA((1)/(2)+ a))* int(GAMMA(t)*GAMMA((1)/(2)+ a - 2*t)*(2)^(t)* (z)^(2*t), t = - I*infinity..I*infinity) |
ParabolicCylinderD[-a - 1/2, z]=Divide[Exp[-Divide[1,4]*(z)^(2)]*(z)^(- a -Divide[1,2]),2*Pi*I*Gamma[Divide[1,2]+ a]]* Integrate[Gamma[t]*Gamma[Divide[1,2]+ a - 2*t]*(2)^(t)* (z)^(2*t), {t, - I*Infinity, I*Infinity}] |
Failure | Failure | Skip | Error |
| 12.5.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{z} = \sqrt{\frac{2}{\pi}}\frac{e^{\frac{1}{4}z^{2}}z^{a-\frac{1}{2}}}{2\pi i\EulerGamma@{\frac{1}{2}-a}}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-a-2t}2^{t}z^{2t}\cos@{\pi t}\diff{t}} | CylinderV(a, z)=sqrt((2)/(Pi))*(exp((1)/(4)*(z)^(2))*(z)^(a -(1)/(2)))/(2*Pi*I*GAMMA((1)/(2)- a))* int(GAMMA(t)*GAMMA((1)/(2)- a - 2*t)*(2)^(t)* (z)^(2*t)* cos(Pi*t), t = - I*infinity..I*infinity) |
Error |
Failure | Error | Skip | - |
| 12.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{-\tfrac{1}{2}}{z} = \WhittakerparaD{0}@{z}} | CylinderU(-(1)/(2), z)= CylinderD(0, z) |
ParabolicCylinderD[--Divide[1,2] - 1/2, z]= ParabolicCylinderD[0, z] |
Successful | Failure | - | Fail
Complex[-0.5535325382896138, 0.3790800612672758] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.5535325382896137, -0.3790800612672758] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.8272649632907405, 3.413116871149585] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.8272649632907406, -3.413116871149585] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 12.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerparaD{0}@{z} = e^{-\frac{1}{4}z^{2}}} | CylinderD(0, z)= exp(-(1)/(4)*(z)^(2)) |
ParabolicCylinderD[0, z]= Exp[-Divide[1,4]*(z)^(2)] |
Successful | Successful | - | - |
| 12.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{-n-\tfrac{1}{2}}{z} = \WhittakerparaD{n}@{z}} | CylinderU(- n -(1)/(2), z)= CylinderD(n, z) |
ParabolicCylinderD[-- n -Divide[1,2] - 1/2, z]= ParabolicCylinderD[n, z] |
Successful | Failure | - | Successful |
| 12.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{-\tfrac{1}{2}}{z} = (\ifrac{2}{\sqrt{\pi}}\,)e^{\frac{1}{4}z^{2}}\DawsonsintF@{z/\sqrt{2}}} | CylinderV(-(1)/(2), z)=((2)/(sqrt(Pi)))* exp((1)/(4)*(z)^(2))*dawson(z/sqrt(2)) |
Error |
Successful | Error | - | - |
| 12.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{\tfrac{1}{2}}{z} = \WhittakerparaD{-1}@{z}} | CylinderU((1)/(2), z)= CylinderD(- 1, z) |
ParabolicCylinderD[-Divide[1,2] - 1/2, z]= ParabolicCylinderD[- 1, z] |
Successful | Successful | - | - |
| 12.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerparaD{-1}@{z} = \sqrt{\tfrac{1}{2}\pi}\,e^{\frac{1}{4}z^{2}}\erfc@{z/\sqrt{2}}} | CylinderD(- 1, z)=sqrt((1)/(2)*Pi)*exp((1)/(4)*(z)^(2))*erfc(z/sqrt(2)) |
ParabolicCylinderD[- 1, z]=Sqrt[Divide[1,2]*Pi]*Exp[Divide[1,4]*(z)^(2)]*Erfc[z/Sqrt[2]] |
Successful | Successful | - | - |
| 12.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{n+\tfrac{1}{2}}{z} = \WhittakerparaD{-n-1}@{z}} | CylinderU(n +(1)/(2), z)= CylinderD(- n - 1, z) |
ParabolicCylinderD[-n +Divide[1,2] - 1/2, z]= ParabolicCylinderD[- n - 1, z] |
Successful | Failure | - | Fail
Complex[-0.033951461448720965, -0.03725090437629219] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.033951461448720965, 0.03725090437629219] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[0.34180963565085953, 2.078059729615049] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.34180963565085953, -2.078059729615049] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 12.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerparaD{-n-1}@{z} = \sqrt{\frac{\pi}{2}}\frac{(-1)^{n}}{n!}e^{-\frac{1}{4}z^{2}}\deriv[n]{\left(e^{\frac{1}{2}z^{2}}\erfc@{z/\sqrt{2}}\right)}{z}} | CylinderD(- n - 1, z)=sqrt((Pi)/(2))*((- 1)^(n))/(factorial(n))*exp(-(1)/(4)*(z)^(2))*diff(exp((1)/(2)*(z)^(2))*erfc(z/sqrt(2)), [z$(n)]) |
ParabolicCylinderD[- n - 1, z]=Sqrt[Divide[Pi,2]]*Divide[(- 1)^(n),(n)!]*Exp[-Divide[1,4]*(z)^(2)]*D[Exp[Divide[1,2]*(z)^(2)]*Erfc[z/Sqrt[2]], {z, n}] |
Failure | Failure | Successful | Successful |
| 12.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{-2}{z} = \frac{z^{5/2}}{4\sqrt{2\pi}}\left(2\!\modBesselK{\frac{1}{4}}@{\tfrac{1}{4}z^{2}}+3\!\modBesselK{\frac{3}{4}}@{\tfrac{1}{4}z^{2}}-\modBesselK{\frac{5}{4}}@{\tfrac{1}{4}z^{2}}\right)} | CylinderU(- 2, z)=((z)^(5/ 2))/(4*sqrt(2*Pi))*(2*BesselK((1)/(4), (1)/(4)*(z)^(2))+ 3*BesselK((3)/(4), (1)/(4)*(z)^(2))- BesselK((5)/(4), (1)/(4)*(z)^(2))) |
ParabolicCylinderD[-- 2 - 1/2, z]=Divide[(z)^(5/ 2),4*Sqrt[2*Pi]]*(2*BesselK[Divide[1,4], Divide[1,4]*(z)^(2)]+ 3*BesselK[Divide[3,4], Divide[1,4]*(z)^(2)]- BesselK[Divide[5,4], Divide[1,4]*(z)^(2)]) |
Failure | Failure | Fail -1.522148495+5.325348960*I <- {z = -2^(1/2)-I*2^(1/2)}-1.522148495-5.325348960*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-2.176847672351804, -0.5824405608621696] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.9645562602658246, -7.19064614909563] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-3.138711633327063, -0.6435109071691986] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.642441416717864, -0.8480286890415233] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{-1}{z} = \frac{z^{3/2}}{2\sqrt{2\pi}}\left(\modBesselK{\frac{1}{4}}@{\tfrac{1}{4}z^{2}}+\modBesselK{\frac{3}{4}}@{\tfrac{1}{4}z^{2}}\right)} | CylinderU(- 1, z)=((z)^(3/ 2))/(2*sqrt(2*Pi))*(BesselK((1)/(4), (1)/(4)*(z)^(2))+ BesselK((3)/(4), (1)/(4)*(z)^(2))) |
ParabolicCylinderD[-- 1 - 1/2, z]=Divide[(z)^(3/ 2),2*Sqrt[2*Pi]]*(BesselK[Divide[1,4], Divide[1,4]*(z)^(2)]+ BesselK[Divide[3,4], Divide[1,4]*(z)^(2)]) |
Failure | Failure | Fail -1.876943385-2.185260402*I <- {z = -2^(1/2)-I*2^(1/2)}-1.876943385+2.185260402*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[-0.5944827156757435, 1.0193657184065432] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.38219130358976394, -5.588839869826917] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5563466766510021, 0.9582953720995141] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.0600764600418031, 0.7537775902271894] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[PreDecrement[1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.7.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{0}{z} = \sqrt{\frac{z}{2\pi}}\modBesselK{\frac{1}{4}}@{\tfrac{1}{4}z^{2}}} | CylinderU(0, z)=sqrt((z)/(2*Pi))*BesselK((1)/(4), (1)/(4)*(z)^(2)) |
ParabolicCylinderD[-0 - 1/2, z]=Sqrt[Divide[z,2*Pi]]*BesselK[Divide[1,4], Divide[1,4]*(z)^(2)] |
Failure | Failure | Fail 2.172244779+.8389494551*I <- {z = -2^(1/2)-I*2^(1/2)}2.172244779-.8389494551*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[2.172244778329958, 0.8389494547782839] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[2.172244778329958, -0.8389494547782839] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 12.7.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{1}{z} = \frac{z^{3/2}}{\sqrt{2\pi}}\left(\modBesselK{\frac{3}{4}}@{\tfrac{1}{4}z^{2}}-\modBesselK{\frac{1}{4}}@{\tfrac{1}{4}z^{2}}\right)} | CylinderU(1, z)=((z)^(3/ 2))/(sqrt(2*Pi))*(BesselK((3)/(4), (1)/(4)*(z)^(2))- BesselK((1)/(4), (1)/(4)*(z)^(2))) |
ParabolicCylinderD[-1 - 1/2, z]=Divide[(z)^(3/ 2),Sqrt[2*Pi]]*(BesselK[Divide[3,4], Divide[1,4]*(z)^(2)]- BesselK[Divide[1,4], Divide[1,4]*(z)^(2)]) |
Failure | Failure | Fail .172418861e-1+4.146422642*I <- {z = -2^(1/2)-I*2^(1/2)}.172418861e-1-4.146422642*I <- {z = -2^(1/2)+I*2^(1/2)} |
Fail
Complex[0.017241884225636828, 4.146422642593135] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.017241884225636828, -4.146422642593135] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 12.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{z} = 2^{-\frac{1}{4}-\frac{1}{2}a}e^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}}} | CylinderU(a, z)= (2)^(-(1)/(4)-(1)/(2)*a)* exp(-(1)/(4)*(z)^(2))*KummerU((1)/(2)*a +(1)/(4), (1)/(2), (1)/(2)*(z)^(2)) |
ParabolicCylinderD[-a - 1/2, z]= (2)^(-Divide[1,4]-Divide[1,2]*a)* Exp[-Divide[1,4]*(z)^(2)]*HypergeometricU[Divide[1,2]*a +Divide[1,4], Divide[1,2], Divide[1,2]*(z)^(2)] |
Failure | Failure | Fail -1.552891817+2.595743470*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.468308225-15.26302300*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}-1.468308225+15.26302300*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-1.552891817-2.595743470*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-1.5528918212023513, 2.595743468355251] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4683082379662649, -15.263023009398044] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-1.4683082379662649, 15.263023009398044] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.5528918212023513, -2.595743468355251] <- {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 |
| 12.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{-\frac{1}{4}-\frac{1}{2}a}e^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{1}{4}}{\tfrac{1}{2}}{\tfrac{1}{2}z^{2}} = 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}}} | (2)^(-(1)/(4)-(1)/(2)*a)* exp(-(1)/(4)*(z)^(2))*KummerU((1)/(2)*a +(1)/(4), (1)/(2), (1)/(2)*(z)^(2))= (2)^(-(3)/(4)-(1)/(2)*a)* z*exp(-(1)/(4)*(z)^(2))*KummerU((1)/(2)*a +(3)/(4), (3)/(2), (1)/(2)*(z)^(2)) |
(2)^(-Divide[1,4]-Divide[1,2]*a)* Exp[-Divide[1,4]*(z)^(2)]*HypergeometricU[Divide[1,2]*a +Divide[1,4], Divide[1,2], Divide[1,2]*(z)^(2)]= (2)^(-Divide[3,4]-Divide[1,2]*a)* z*Exp[-Divide[1,4]*(z)^(2)]*HypergeometricU[Divide[1,2]*a +Divide[3,4], Divide[3,2], Divide[1,2]*(z)^(2)] |
Failure | Failure | Fail -.8240048131+.2272943481*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}.1685356209+.1817412146*I <- {a = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}.1685356209-.1817412146*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}-.8240048131-.2272943481*I <- {a = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-0.8240048125018726, 0.22729434917761066] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.1685356207165261, 0.1817412145670384] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.1685356207165261, -0.1817412145670384] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.8240048125018726, -0.22729434917761066] <- {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 |
| 12.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = 2^{-\frac{1}{2}a}z^{-\frac{1}{2}}\WhittakerconfhyperW{-\frac{1}{2}a}{+\frac{1}{4}}@{\tfrac{1}{2}z^{2}}} | (2)^(-(3)/(4)-(1)/(2)*a)* z*exp(-(1)/(4)*(z)^(2))*KummerU((1)/(2)*a +(3)/(4), (3)/(2), (1)/(2)*(z)^(2))= (2)^(-(1)/(2)*a)* (z)^(-(1)/(2))* WhittakerW(-(1)/(2)*a, +(1)/(4), (1)/(2)*(z)^(2)) |
(2)^(-Divide[3,4]-Divide[1,2]*a)* z*Exp[-Divide[1,4]*(z)^(2)]*HypergeometricU[Divide[1,2]*a +Divide[3,4], Divide[3,2], Divide[1,2]*(z)^(2)]= (2)^(-Divide[1,2]*a)* (z)^(-Divide[1,2])* WhittakerW[-Divide[1,2]*a, +Divide[1,4], Divide[1,2]*(z)^(2)] |
Failure | Failure | Skip | Fail
Complex[0.5256495808397417, 0.2983552316621309] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.17513841764178226, -0.006602796925256171] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.17513841764178226, 0.006602796925256171] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.5256495808397417, -0.2983552316621309] <- {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 |
| 12.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}\KummerconfhyperU@{\tfrac{1}{2}a+\tfrac{3}{4}}{\tfrac{3}{2}}{\tfrac{1}{2}z^{2}} = 2^{-\frac{1}{2}a}z^{-\frac{1}{2}}\WhittakerconfhyperW{-\frac{1}{2}a}{-\frac{1}{4}}@{\tfrac{1}{2}z^{2}}} | (2)^(-(3)/(4)-(1)/(2)*a)* z*exp(-(1)/(4)*(z)^(2))*KummerU((1)/(2)*a +(3)/(4), (3)/(2), (1)/(2)*(z)^(2))= (2)^(-(1)/(2)*a)* (z)^(-(1)/(2))* WhittakerW(-(1)/(2)*a, -(1)/(4), (1)/(2)*(z)^(2)) |
(2)^(-Divide[3,4]-Divide[1,2]*a)* z*Exp[-Divide[1,4]*(z)^(2)]*HypergeometricU[Divide[1,2]*a +Divide[3,4], Divide[3,2], Divide[1,2]*(z)^(2)]= (2)^(-Divide[1,2]*a)* (z)^(-Divide[1,2])* WhittakerW[-Divide[1,2]*a, -Divide[1,4], Divide[1,2]*(z)^(2)] |
Failure | Failure | Skip | Fail
Complex[0.5256495808397417, 0.2983552316621309] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.17513841764178226, -0.0066027969252561575] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.17513841764178226, 0.0066027969252561575] <- {Rule[a, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[0.5256495808397417, -0.2983552316621309] <- {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 |
| 12.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\paraU@{a}{z}-\paraU@{a-1}{z}+(a+\tfrac{1}{2})\paraU@{a+1}{z} = 0} | z*CylinderU(a, z)- CylinderU(a - 1, z)+(a +(1)/(2))* CylinderU(a + 1, z)= 0 |
z*ParabolicCylinderD[-a - 1/2, z]- ParabolicCylinderD[-a - 1 - 1/2, z]+(a +Divide[1,2])* ParabolicCylinderD[-a + 1 - 1/2, z]= 0 |
Successful | Failure | - | Fail
Complex[-2.212392415520596, -2.7835289048360865] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.47884522381711175, 0.5350814275558994] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.550805211617881, -3.493113886500579] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[73.63864596732188, 31.232726056290662] <- {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 |
| 12.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU'@{a}{z}+\tfrac{1}{2}z\paraU@{a}{z}+(a+\tfrac{1}{2})\paraU@{a+1}{z} = 0} | subs( temp=z, diff( CylinderU(a, temp), temp$(1) ) )+(1)/(2)*z*CylinderU(a, z)+(a +(1)/(2))* CylinderU(a + 1, z)= 0 |
(D[ParabolicCylinderD[-a - 1/2, temp], {temp, 1}]/.temp-> z)+Divide[1,2]*z*ParabolicCylinderD[-a - 1/2, z]+(a +Divide[1,2])* ParabolicCylinderD[-a + 1 - 1/2, z]= 0 |
Successful | Failure | - | Fail
Complex[-1.2227570491036914, -2.308624400336341] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.2737322573556834, 0.45100801175309346] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[3.0354158227028893, -2.0443578293881037] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[48.97674308818175, 32.48331095383318] <- {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 |
| 12.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU'@{a}{z}-\tfrac{1}{2}z\paraU@{a}{z}+\paraU@{a-1}{z} = 0} | subs( temp=z, diff( CylinderU(a, temp), temp$(1) ) )-(1)/(2)*z*CylinderU(a, z)+ CylinderU(a - 1, z)= 0 |
(D[ParabolicCylinderD[-a - 1/2, temp], {temp, 1}]/.temp-> z)-Divide[1,2]*z*ParabolicCylinderD[-a - 1/2, z]+ ParabolicCylinderD[-a - 1 - 1/2, z]= 0 |
Successful | Failure | - | Fail
Complex[0.9896353664169044, 0.4749045044997455] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-0.20511296646142838, -0.0840734158028059] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-0.5153893889149921, 1.4487560571124753] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-24.66190287914013, 1.250584897542514] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\paraU'@{a}{z}+\paraU@{a-1}{z}+(a+\tfrac{1}{2})\paraU@{a+1}{z} = 0} | 2*subs( temp=z, diff( CylinderU(a, temp), temp$(1) ) )+ CylinderU(a - 1, z)+(a +(1)/(2))* CylinderU(a + 1, z)= 0 |
2*(D[ParabolicCylinderD[-a - 1/2, temp], {temp, 1}]/.temp-> z)+ ParabolicCylinderD[-a - 1 - 1/2, z]+(a +Divide[1,2])* ParabolicCylinderD[-a + 1 - 1/2, z]= 0 |
Successful | Failure | - | Fail
Complex[-0.233121682686787, -1.8337198958365952] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.06861929089425498, 0.36693459595028755] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.520026433787896, -0.5956017722756277] <- {Rule[a, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[24.314840209041613, 33.733895851375685] <- {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 |
| 12.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\paraV@{a}{z}-\paraV@{a+1}{z}+(a-\tfrac{1}{2})\paraV@{a-1}{z} = 0} | z*CylinderV(a, z)- CylinderV(a + 1, z)+(a -(1)/(2))* CylinderV(a - 1, z)= 0 |
Error |
Successful | Error | - | - |
| 12.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV'@{a}{z}-\tfrac{1}{2}z\paraV@{a}{z}-(a-\tfrac{1}{2})\paraV@{a-1}{z} = 0} | subs( temp=z, diff( CylinderV(a, temp), temp$(1) ) )-(1)/(2)*z*CylinderV(a, z)-(a -(1)/(2))* CylinderV(a - 1, z)= 0 |
Error |
Successful | Error | - | - |
| 12.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV'@{a}{z}+\tfrac{1}{2}z\paraV@{a}{z}-\paraV@{a+1}{z} = 0} | subs( temp=z, diff( CylinderV(a, temp), temp$(1) ) )+(1)/(2)*z*CylinderV(a, z)- CylinderV(a + 1, z)= 0 |
Error |
Successful | Error | - | - |
| 12.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\paraV'@{a}{z}-\paraV@{a+1}{z}-(a-\tfrac{1}{2})\paraV@{a-1}{z} = 0} | 2*subs( temp=z, diff( CylinderV(a, temp), temp$(1) ) )- CylinderV(a + 1, z)-(a -(1)/(2))* CylinderV(a - 1, z)= 0 |
Error |
Successful | Error | - | - |
| 12.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[m]{}{z}\left(e^{\frac{1}{4}z^{2}}\paraU@{a}{z}\right) = (-1)^{m}\Pochhammersym{\tfrac{1}{2}+a}{m}e^{\frac{1}{4}z^{2}}\paraU@{a+m}{z}} | diff(exp((1)/(4)*(z)^(2))*CylinderU(a, z), [z$(m)])=(- 1)^(m)* pochhammer((1)/(2)+ a, m)*exp((1)/(4)*(z)^(2))*CylinderU(a + m, z) |
D[Exp[Divide[1,4]*(z)^(2)]*ParabolicCylinderD[-a - 1/2, z], {z, m}]=(- 1)^(m)* Pochhammer[Divide[1,2]+ a, m]*Exp[Divide[1,4]*(z)^(2)]*ParabolicCylinderD[-a + m - 1/2, z] |
Failure | Failure | Skip | Skip |
| 12.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[m]{}{z}\left(e^{-\frac{1}{4}z^{2}}\paraU@{a}{z}\right) = (-1)^{m}e^{-\frac{1}{4}z^{2}}\paraU@{a-m}{z}} | diff(exp(-(1)/(4)*(z)^(2))*CylinderU(a, z), [z$(m)])=(- 1)^(m)* exp(-(1)/(4)*(z)^(2))*CylinderU(a - m, z) |
D[Exp[-Divide[1,4]*(z)^(2)]*ParabolicCylinderD[-a - 1/2, z], {z, m}]=(- 1)^(m)* Exp[-Divide[1,4]*(z)^(2)]*ParabolicCylinderD[-a - m - 1/2, z] |
Failure | Failure | Skip | Skip |
| 12.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[m]{}{z}\left(e^{\frac{1}{4}z^{2}}\paraV@{a}{z}\right) = e^{\frac{1}{4}z^{2}}\paraV@{a+m}{z}} | diff(exp((1)/(4)*(z)^(2))*CylinderV(a, z), [z$(m)])= exp((1)/(4)*(z)^(2))*CylinderV(a + m, z) |
Error |
Failure | Error | Skip | - |
| 12.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[m]{}{z}\left(e^{-\frac{1}{4}z^{2}}\paraV@{a}{z}\right) = (-1)^{m}\Pochhammersym{\tfrac{1}{2}-a}{m}e^{-\frac{1}{4}z^{2}}\paraV@{a-m}{z}} | diff(exp(-(1)/(4)*(z)^(2))*CylinderV(a, z), [z$(m)])=(- 1)^(m)* pochhammer((1)/(2)- a, m)*exp(-(1)/(4)*(z)^(2))*CylinderV(a - m, z) |
Error |
Failure | Error | Skip | - |
| 12.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{t} = \mu^{4}(t^{2}+ 1)w} | diff(w, [t$(2)])= (mu)^(4)*((t)^(2)+ 1)* w |
D[w, {t, 2}]= (\[Mu])^(4)*((t)^(2)+ 1)* w |
Failure | Failure | Fail -67.88225086+113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}113.1370848+67.88225084*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}67.88225084-113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-113.1370848-67.88225084*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-67.88225099390857, 113.13708498984761] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-67.88225099390857, 113.13708498984761] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-67.88225099390857, 113.13708498984761] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-67.88225099390857, 113.13708498984761] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{t} = \mu^{4}(t^{2}- 1)w} | diff(w, [t$(2)])= (mu)^(4)*((t)^(2)- 1)* w |
D[w, {t, 2}]= (\[Mu])^(4)*((t)^(2)- 1)* w |
Failure | Failure | Fail -113.1370848+67.88225086*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}67.88225084+113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}113.1370848-67.88225084*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}-67.88225084-113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[-113.13708498984761, 67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[-113.13708498984761, 67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-113.13708498984761, 67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-113.13708498984761, 67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{1}{4}t^{2}}t^{\mu-1}\paraU@{a}{t}\diff{t} = \frac{\sqrt{\pi}2^{-\frac{1}{2}(\mu+a+\frac{1}{2})}\EulerGamma@{\mu}}{\EulerGamma@{\frac{1}{2}(\mu+a+\frac{3}{2})}}} | int(exp(-(1)/(4)*(t)^(2))*(t)^(mu - 1)* CylinderU(a, t), t = 0..infinity)=(sqrt(Pi)*(2)^(-(1)/(2)*(mu + a +(1)/(2)))* GAMMA(mu))/(GAMMA((1)/(2)*(mu + a +(3)/(2)))) |
Integrate[Exp[-Divide[1,4]*(t)^(2)]*(t)^(\[Mu]- 1)* ParabolicCylinderD[-a - 1/2, t], {t, 0, Infinity}]=Divide[Sqrt[Pi]*(2)^(-Divide[1,2]*(\[Mu]+ a +Divide[1,2]))* Gamma[\[Mu]],Gamma[Divide[1,2]*(\[Mu]+ a +Divide[3,2])]] |
Failure | Failure | Skip | Error |
| 12.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{3}{4}t^{2}}t^{-a-\frac{3}{2}}\paraU@{a}{t}\diff{t} = 2^{\frac{1}{4}+\frac{1}{2}a}\EulerGamma@{-a-\tfrac{1}{2}}\cos@{(\tfrac{1}{4}a+\tfrac{1}{8})\pi}} | int(exp(-(3)/(4)*(t)^(2))*(t)^(- a -(3)/(2))* CylinderU(a, t), t = 0..infinity)= (2)^((1)/(4)+(1)/(2)*a)* GAMMA(- a -(1)/(2))*cos(((1)/(4)*a +(1)/(8))* Pi) |
Integrate[Exp[-Divide[3,4]*(t)^(2)]*(t)^(- a -Divide[3,2])* ParabolicCylinderD[-a - 1/2, t], {t, 0, Infinity}]= (2)^(Divide[1,4]+Divide[1,2]*a)* Gamma[- a -Divide[1,2]]*Cos[(Divide[1,4]*a +Divide[1,8])* Pi] |
Failure | Failure | Skip | Successful |
| 12.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{1}{4}t^{2}}t^{-a-\frac{1}{2}}(x^{2}+t^{2})^{-1}\paraU@{a}{t}\diff{t} = \sqrt{\pi/2}\EulerGamma@{\tfrac{1}{2}-a}x^{-a-\frac{3}{2}}e^{\frac{1}{4}x^{2}}\paraU@{-a}{x}} | int(exp(-(1)/(4)*(t)^(2))*(t)^(- a -(1)/(2))*((x)^(2)+ (t)^(2))^(- 1)* CylinderU(a, t), t = 0..infinity)=sqrt(Pi/ 2)*GAMMA((1)/(2)- a)*(x)^(- a -(3)/(2))* exp((1)/(4)*(x)^(2))*CylinderU(- a, x) |
Integrate[Exp[-Divide[1,4]*(t)^(2)]*(t)^(- a -Divide[1,2])*((x)^(2)+ (t)^(2))^(- 1)* ParabolicCylinderD[-a - 1/2, t], {t, 0, Infinity}]=Sqrt[Pi/ 2]*Gamma[Divide[1,2]- a]*(x)^(- a -Divide[3,2])* Exp[Divide[1,4]*(x)^(2)]*ParabolicCylinderD[-- a - 1/2, x] |
Failure | Failure | Skip | Error |
| 12.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{x+y} = e^{\frac{1}{2}xy+\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}\frac{(-y)^{m}}{m!}\paraU@{a-m}{x}} | CylinderU(a, x + y)= exp((1)/(2)*x*y +(1)/(4)*(y)^(2))*sum(((- y)^(m))/(factorial(m))*CylinderU(a - m, x), m = 0..infinity) |
ParabolicCylinderD[-a - 1/2, x + y]= Exp[Divide[1,2]*x*y +Divide[1,4]*(y)^(2)]*Sum[Divide[(- y)^(m),(m)!]*ParabolicCylinderD[-a - m - 1/2, x], {m, 0, Infinity}] |
Failure | Failure | Skip | Skip |
| 12.13.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraU@{a}{x\cos@@{t}+y\sin@@{t}}\\ = e^{\frac{1}{4}(x\sin@@{t}-y\cos@@{t})^{2}}\*\sum_{m=0}^{\infty}\binom{-a-\tfrac{1}{2}}{m}(\tan@@{t})^{m}\paraU@{m+a}{x}\paraU@{-m-\tfrac{1}{2}}{y}} | CylinderU(a, x*cos(t)+ y*sin(t))= exp((1)/(4)*(x*sin(t)- y*cos(t))^(2))* sum(binomial(- a -(1)/(2),m)*(tan(t))^(m)* CylinderU(m + a, x)*CylinderU(- m -(1)/(2), y), m = 0..infinity) |
ParabolicCylinderD[-a - 1/2, x*Cos[t]+ y*Sin[t]]= Exp[Divide[1,4]*(x*Sin[t]- y*Cos[t])^(2)]* Sum[Binomial[- a -Divide[1,2],m]*(Tan[t])^(m)* ParabolicCylinderD[-m + a - 1/2, x]*ParabolicCylinderD[-- m -Divide[1,2] - 1/2, y], {m, 0, Infinity}] |
Error | Error | - | - |
| 12.14.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(a,x) = e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}}} | w[1]*(a , x)= exp(-(1)/(4)*I*(x)^(2))*KummerM((1)/(4)-(1)/(2)*I*a, (1)/(2), (1)/(2)*I*(x)^(2)) |
Subscript[w, 1]*(a , x)= Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]-Divide[1,2]*I*a, Divide[1,2], Divide[1,2]*I*(x)^(2)] |
Failure | Failure | Error | Error |
| 12.14.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}-\tfrac{1}{2}ia}{\tfrac{1}{2}}{\tfrac{1}{2}ix^{2}} = e^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{1}{4}+\tfrac{1}{2}ia}{\tfrac{1}{2}}{-\tfrac{1}{2}ix^{2}}} | exp(-(1)/(4)*I*(x)^(2))*KummerM((1)/(4)-(1)/(2)*I*a, (1)/(2), (1)/(2)*I*(x)^(2))= exp((1)/(4)*I*(x)^(2))*KummerM((1)/(4)+(1)/(2)*I*a, (1)/(2), -(1)/(2)*I*(x)^(2)) |
Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]-Divide[1,2]*I*a, Divide[1,2], Divide[1,2]*I*(x)^(2)]= Exp[Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[1,4]+Divide[1,2]*I*a, Divide[1,2], -Divide[1,2]*I*(x)^(2)] |
Failure | Successful | Successful | - |
| 12.14.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(a,x) = xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}}} | w[2]*(a , x)= x*exp(-(1)/(4)*I*(x)^(2))*KummerM((3)/(4)-(1)/(2)*I*a, (3)/(2), (1)/(2)*I*(x)^(2)) |
Subscript[w, 2]*(a , x)= x*Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]-Divide[1,2]*I*a, Divide[3,2], Divide[1,2]*I*(x)^(2)] |
Failure | Failure | Error | Error |
| 12.14.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle xe^{-\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}-\tfrac{1}{2}ia}{\tfrac{3}{2}}{\tfrac{1}{2}ix^{2}} = xe^{\frac{1}{4}ix^{2}}\KummerconfhyperM@{\tfrac{3}{4}+\tfrac{1}{2}ia}{\tfrac{3}{2}}{-\tfrac{1}{2}ix^{2}}} | x*exp(-(1)/(4)*I*(x)^(2))*KummerM((3)/(4)-(1)/(2)*I*a, (3)/(2), (1)/(2)*I*(x)^(2))= x*exp((1)/(4)*I*(x)^(2))*KummerM((3)/(4)+(1)/(2)*I*a, (3)/(2), -(1)/(2)*I*(x)^(2)) |
x*Exp[-Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]-Divide[1,2]*I*a, Divide[3,2], Divide[1,2]*I*(x)^(2)]= x*Exp[Divide[1,4]*I*(x)^(2)]*Hypergeometric1F1[Divide[3,4]+Divide[1,2]*I*a, Divide[3,2], -Divide[1,2]*I*(x)^(2)] |
Failure | Successful | Successful | - |
| 12.14.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{t} = \mu^{4}(1-t^{2})w} | diff(w, [t$(2)])= (mu)^(4)*(1 - (t)^(2))* w |
D[w, {t, 2}]= (\[Mu])^(4)*(1 - (t)^(2))* w |
Failure | Failure | Fail 113.1370848-67.88225086*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2)}-67.88225084-113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2)}-113.1370848+67.88225084*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)-I*2^(1/2)}67.88225084+113.1370848*I <- {mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2), w = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Fail
Complex[113.13708498984761, -67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[113.13708498984761, -67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[113.13708498984761, -67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[113.13708498984761, -67.88225099390857] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 12.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(\nu+\lambda^{-1}-\lambda^{-2}z^{\lambda}\right)w = 0} | diff(w, [z$(2)])+(nu + (lambda)^(- 1)- (lambda)^(- 2)* (z)^(lambda))* w = 0 |
D[w, {z, 2}]+(\[Nu]+ (\[Lambda])^(- 1)- (\[Lambda])^(- 2)* (z)^(\[Lambda]))* w = 0 |
Failure | Failure | Fail .8849712009+3.576499096*I <- {lambda = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}-1.464705312+7.209161093*I <- {lambda = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}38.31009603+4.160077343*I <- {lambda = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}1.044102247+4.017893257*I <- {lambda = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}... skip entries to safe data |
Skip |
| 12.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\xi^{2}+\eta^{2}}\left(\pderiv[2]{w}{\xi}+\pderiv[2]{w}{\eta}\right)+\pderiv[2]{w}{\zeta}+k^{2}w = 0} | (1)/((xi)^(2)+ (eta)^(2))*(diff(w, [xi$(2)])+ diff(w, [eta$(2)]))+ diff(w, [zeta$(2)])+ (k)^(2)* w = 0 |
Divide[1,(\[Xi])^(2)+ (\[Eta])^(2)]*(D[w, {\[Xi], 2}]+ D[w, {\[Eta], 2}])+ D[w, {\[zeta], 2}]+ (k)^(2)* w = 0 |
Failure | Failure | Fail 1.414213562+1.414213562*I <- {w = 2^(1/2)+I*2^(1/2), k = 1}5.656854248+5.656854248*I <- {w = 2^(1/2)+I*2^(1/2), k = 2}12.72792206+12.72792206*I <- {w = 2^(1/2)+I*2^(1/2), k = 3}1.414213562-1.414213562*I <- {w = 2^(1/2)-I*2^(1/2), k = 1}... skip entries to safe data |
Error |
| 12.17#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{\paraU}{\xi}+\left(\sigma\xi^{2}+\lambda\right)\paraU = 0} | diff(CylinderU(xi, +), [(sigma*(xi)^(2)+ lambda)*$(2)])*CylinderU(=, 0) |
D[ParabolicCylinderD[-\[Xi] - 1/2, +], {(\[Sigma]*(\[Xi])^(2)+ \[Lambda])*, 2}]*ParabolicCylinderD[-= - 1/2, 0] |
Error | Error | - | - |
| 12.17#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{\paraV}{\eta}+\left(\sigma\eta^{2}-\lambda\right)\paraV = 0} | diff(CylinderV(eta, +), [(sigma*(eta)^(2)- lambda)*$(2)])*CylinderV(=, 0) |
Error |
Error | Error | - | - |