Parabolic Cylinder Functions - 12.15 Generalized Parabolic Cylinder Functions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 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}
\deriv[2]{w}{z}+\left(\nu+\lambda^{-1}-\lambda^{-2}z^{\lambda}\right)w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed [300 / 300] Result: .7322275248+.9199723429*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
Result: 1.402820433+.5288298490*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[0.7322275239543282, 0.91997234266967]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-0.6337978798301105, 0.5539469388852316]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |