Parabolic Cylinder Functions - 12.17 Physical Applications

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
12.17.E4	${\displaystyle{\displaystyle\frac{1}{\xi^{2}+\eta^{2}}\left(\frac{{\partial}^{2}w}{{\partial\xi}^{2}}+\frac{{\partial}^{2}w}{{\partial\eta}^{2}}\right)+\frac{{\partial}^{2}w}{{\partial\zeta}^{2}}+k^{2}w=0}}$ \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	Failed [300 / 300] Result: .8660254040+.5000000000*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, k = 1} Result: 3.464101616+2.*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.8660254037844387, 0.49999999999999994] Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[3.464101615137755, 1.9999999999999998] Test Values: {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data