Spheroidal Wave Functions - 31.2 Differential Equations
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 31.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+\left(\frac{\gamma}{z}+\frac{\delta}{z-1}+\frac{\epsilon}{z-a}\right)\deriv{w}{z}+\frac{\alpha\beta z-q}{z(z-1)(z-a)}w = 0}
\deriv[2]{w}{z}+\left(\frac{\gamma}{z}+\frac{\delta}{z-1}+\frac{\epsilon}{z-a}\right)\deriv{w}{z}+\frac{\alpha\beta z-q}{z(z-1)(z-a)}w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha+\beta+1 = \gamma+\delta+\epsilon} | diff(w, [z$(2)])+((gamma)/(z)+(delta)/(z - 1)+(epsilon)/(z - a))*diff(w, z)+(alpha*beta*z - q)/(z*(z - 1)*(z - a))*w = 0
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D[w, {z, 2}]+(Divide[\[Gamma],z]+Divide[\[Delta],z - 1]+Divide[\[Epsilon],z - a])*D[w, z]+Divide[\[Alpha]*\[Beta]*z - q,z*(z - 1)*(z - a)]*w == 0
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Failure | Failure | Manual Skip! | Skipped - Because timed out |
| 31.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = z^{-\gamma/2}(z-1)^{-\delta/2}(z-a)^{-\epsilon/2}W(z)}
w(z) = z^{-\gamma/2}(z-1)^{-\delta/2}(z-a)^{-\epsilon/2}W(z) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | w(z) = (z)^(- gamma/2)*(z - 1)^(- delta/2)*(z - a)^(- epsilon/2)* W(z) |
w[z] == (z)^(- \[Gamma]/2)*(z - 1)^(- \[Delta]/2)*(z - a)^(- \[Epsilon]/2)* W[z] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 31.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \sin^{2}@@{\theta}}
z = \sin^{2}@@{\theta} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | z = (sin(theta))^(2)
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z == (Sin[\[Theta]])^(2)
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Failure | Failure | Failed [70 / 70] Result: .2421495608-.799774456e-1*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
Result: -1.123875843+.2860479584*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Failed [70 / 70]
Result: Complex[0.24214956105065266, -0.07997744567545023]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[1.1534018595635964, 1.651829143585053]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 31.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{\theta}+\left({(2\gamma-1)\cot@@{\theta}-(2\delta-1)\tan@@{\theta}}-\frac{\epsilon\sin@{2\theta}}{a-\sin^{2}@@{\theta}}\right)\deriv{w}{\theta}+4\frac{\alpha\beta\sin^{2}@@{\theta}-q}{a-\sin^{2}@@{\theta}}w = 0}
\deriv[2]{w}{\theta}+\left({(2\gamma-1)\cot@@{\theta}-(2\delta-1)\tan@@{\theta}}-\frac{\epsilon\sin@{2\theta}}{a-\sin^{2}@@{\theta}}\right)\deriv{w}{\theta}+4\frac{\alpha\beta\sin^{2}@@{\theta}-q}{a-\sin^{2}@@{\theta}}w = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff(w, [theta$(2)])+((2*gamma - 1)*cot(theta)-(2*delta - 1)*tan(theta)-(epsilon*sin(2*theta))/(a - (sin(theta))^(2)))*diff(w, theta)+ 4*(alpha*beta*(sin(theta))^(2)- q)/(a - (sin(theta))^(2))*w = 0
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D[w, {\[Theta], 2}]+((2*\[Gamma]- 1)*Cot[\[Theta]]-(2*\[Delta]- 1)*Tan[\[Theta]]-Divide[\[Epsilon]*Sin[2*\[Theta]],a - (Sin[\[Theta]])^(2)])*D[w, \[Theta]]+ 4*Divide[\[Alpha]*\[Beta]*(Sin[\[Theta]])^(2)- q,a - (Sin[\[Theta]])^(2)]*w == 0
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Failure | Failure | Manual Skip! | Skipped - Because timed out |