Lamé Functions - 29.11 Lamé Wave Equation

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
29.11.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(h-\nu(\nu+1)k^{2}{\operatorname{sn}^{2}}\left(z,k\right)+k^{2}\omega^{2}{\operatorname{sn}^{4}}\left(z,k\right))w=0}}$ \deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0		diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2)+ (k)^(2)* (omega)^(2)* (JacobiSN(z, k))^(4))*w = 0	D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (k)^(2)* \[Omega]^(2)* (JacobiSN[z, (k)^2])^(4))*w == 0	Failure	Failure	Failed [300 / 300] Result: .4970479804-.2136667430*I Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 1} Result: -.5039614158-1.687364305*I Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.4970479802306743, -0.21366674241821534] Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.5039614145885605, -1.6873643054323533] Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data