30.14

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
30.14#Ex4	${\displaystyle{\displaystyle 0<\xi}}$ 0 < \xi		0 < xi	0 < \[Xi]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14#Ex5	${\displaystyle{\displaystyle-1<\eta}}$ -1 < \eta		- 1 < eta	- 1 < \[Eta]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14#Ex6	${\displaystyle{\displaystyle 0\leq\phi}}$ 0 \leq \phi		0 <= phi	0 <= \[Phi]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14.E3	${\displaystyle{\displaystyle h_{\xi}^{2}=\frac{c^{2}(\xi^{2}+\eta^{2})}{1+\xi^{2}}}}$ h_{\xi}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1+\xi^{2}}		(h[xi])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 + (xi)^(2))	(Subscript[h, \[Xi]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 + \[Xi]^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14.E4	${\displaystyle{\displaystyle h_{\eta}^{2}=\frac{c^{2}(\xi^{2}+\eta^{2})}{1-\eta^{2}}}}$ h_{\eta}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1-\eta^{2}}		(h[eta])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 - (eta)^(2))	(Subscript[h, \[Eta]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 - \[Eta]^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14.E5	${\displaystyle{\displaystyle h_{\phi}^{2}=c^{2}(\xi^{2}+1)(1-\eta^{2})}}$ h_{\phi}^{2} = c^{2}(\xi^{2}+1)(1-\eta^{2})		(h[phi])^(2) = (c)^(2)*((xi)^(2)+ 1)*(1 - (eta)^(2))	(Subscript[h, \[Phi]])^(2) == (c)^(2)*(\[Xi]^(2)+ 1)*(1 - \[Eta]^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
30.14.E7	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}\xi}\left((1+\xi^{2})\frac{\mathrm{d}w_{1}}{\mathrm{d}\xi}\right)-\left(\lambda+\gamma^{2}(1+\xi^{2})-\frac{\mu^{2}}{1+\xi^{2}}\right)w_{1}=0}}$ \deriv{}{\xi}\left((1+\xi^{2})\deriv{w_{1}}{\xi}\right)-\left(\lambda+\gamma^{2}(1+\xi^{2})-\frac{\mu^{2}}{1+\xi^{2}}\right)w_{1} = 0		diff(((1 + (xi)^(2))*diff(w[1], xi))-(lambda + (gamma)^(2)*(1 + (xi)^(2))-((mu)^(2))/(1 + (xi)^(2)))*w[1], xi) = 0	D[((1 + \[Xi]^(2))*D[Subscript[w, 1], \[Xi]])-(\[Lambda]+ \[Gamma]^(2)*(1 + \[Xi]^(2))-Divide[\[Mu]^(2),1 + \[Xi]^(2)])*Subscript[w, 1], \[Xi]] == 0	Failure	Failure	Failed [260 / 300] Result: -.6665112581-1.154431362*I Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I} Result: 1.154431362-.6665112581*I Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.6666666666666664, -2.309401076758503] Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.309401076758503, 0.6666666666666662] Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
30.14.E8	${\displaystyle{\displaystyle w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(i\xi,\gamma\right)+b_{1}S^{m(2)}_{n}\left(i\xi,\gamma\right)}}$ w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{i\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{i\xi}{\gamma}		Error	Subscript[w, 1][\[Xi]] == Subscript[a, 1]*SpheroidalS1[n, m, I*\[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, I*\[Xi], \[Gamma]]	Missing Macro Error	Failure	-	Skipped - Because timed out
30.14.E9	${\displaystyle{\displaystyle S^{m(1)}_{n}\left(\mathrm{i}\xi_{0},\gamma\right)=0}}$ \radsphwaveS{m}{1}{n}@{\iunit\xi_{0}}{\gamma} = 0		Error	SpheroidalS1[n, m, I*Subscript[\[Xi], 0], \[Gamma]] == 0	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-0.30414296182717676, -0.005578569442222112] Test Values: {Rule[j, 4], Rule[m, 1], Rule[n, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.05539464168732451, -0.030004541724887247] Test Values: {Rule[j, 4], Rule[m, 1], Rule[n, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data