Mathieu Functions and Hill’s Equation - 28.5 Second Solutions ,
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (C_{n}(q))^{2}\int_{0}^{2\pi}(f_{n}(x,q))^{2}\diff{x} = (S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x}}
(C_{n}(q))^{2}\int_{0}^{2\pi}(f_{n}(x,q))^{2}\diff{x} = (S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (C[n](q))^(2)* int((f[n](x , q))^(2), x = 0..2*Pi) = (S[n](q))^(2)* int((g[n](x , q))^(2), x = 0..2*Pi)
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(Subscript[C, n][q])^(2)* Integrate[(Subscript[f, n][x , q])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == (Subscript[S, n][q])^(2)* Integrate[(Subscript[g, n][x , q])^(2), {x, 0, 2*Pi}, GenerateConditions->None]
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Failure | Failure | Failed [240 / 300] Result: -165.3668092+.1069227006e-6*I
Test Values: {q = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, g[n] = -1/2+1/2*I*3^(1/2), n = 1}
Result: -165.3668092+.1069227006e-6*I
Test Values: {q = 1/2*3^(1/2)+1/2*I, C[n] = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, f[n] = 1/2*3^(1/2)+1/2*I, g[n] = -1/2+1/2*I*3^(1/2), n = 2}
... skip entries to safe data |
Error |
| 28.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} = \pi}
(S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} = \pi |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (S[n](q))^(2)* int((g[n](x , q))^(2), x = 0..2*Pi) = Pi
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(Subscript[S, n][q])^(2)* Integrate[(Subscript[g, n][x , q])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi
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Failure | Failure | Failed [300 / 300] Result: -85.82499725+.5347530766e-7*I
Test Values: {q = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: -85.82499725+.5347530766e-7*I
Test Values: {q = 1/2*3^(1/2)+1/2*I, S[n] = 1/2*3^(1/2)+1/2*I, g[n] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Error |
| 28.5#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{2m}(-q) = C_{2m}(q)}
C_{2m}(-q) = C_{2m}(q) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[2*m](- q) = C[2*m](q) |
Subscript[C, 2*m][- q] == Subscript[C, 2*m][q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.5#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{2m+1}(-q) = S_{2m+1}(q)}
C_{2m+1}(-q) = S_{2m+1}(q) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | C[2*m + 1](- q) = S[2*m + 1](q) |
Subscript[C, 2*m + 1][- q] == Subscript[S, 2*m + 1][q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.5#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{2m+2}(-q) = S_{2m+2}(q)}
S_{2m+2}(-q) = S_{2m+2}(q) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | S[2*m + 2](- q) = S[2*m + 2](q) |
Subscript[S, 2*m + 2][- q] == Subscript[S, 2*m + 2][q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |