Mathieu Functions and Hill’s Equation - 28.11 Expansions in Series of Mathieu Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 = 2\sum_{n=0}^{\infty}A_{0}^{2n}(q)\Mathieuce{2n}@{z}{q}}
1 = 2\sum_{n=0}^{\infty}A_{0}^{2n}(q)\Mathieuce{2n}@{z}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 1 = 2*sum((A[0])^(2*n)(q)* MathieuCE(2*n, q, z), n = 0..infinity)
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1 == 2*Sum[(Subscript[A, 0])^(2*n)[q]* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 28.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{2mz} = \sum_{n=0}^{\infty}A_{2m}^{2n}(q)\Mathieuce{2n}@{z}{q}}
\cos@@{2mz} = \sum_{n=0}^{\infty}A_{2m}^{2n}(q)\Mathieuce{2n}@{z}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m \neq 0} | cos(2*m*z) = sum((A[2*m])^(2*n)(q)* MathieuCE(2*n, q, z), n = 0..infinity)
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Cos[2*m*z] == Sum[(Subscript[A, 2*m])^(2*n)[q]* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 28.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{(2m+1)z} = \sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)\Mathieuce{2n+1}@{z}{q}}
\cos@@{(2m+1)z} = \sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)\Mathieuce{2n+1}@{z}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos((2*m + 1)*z) = sum((A[2*m + 1])^(2*n + 1)(q)* MathieuCE(2*n + 1, q, z), n = 0..infinity)
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Cos[(2*m + 1)*z] == Sum[(Subscript[A, 2*m + 1])^(2*n + 1)[q]* MathieuC[2*n + 1, q, z], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 28.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{(2m+1)z} = \sum_{n=0}^{\infty}B_{2m+1}^{2n+1}(q)\Mathieuse{2n+1}@{z}{q}}
\sin@@{(2m+1)z} = \sum_{n=0}^{\infty}B_{2m+1}^{2n+1}(q)\Mathieuse{2n+1}@{z}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin((2*m + 1)*z) = sum((B[2*m + 1])^(2*n + 1)(q)* MathieuSE(2*n + 1, q, z), n = 0..infinity)
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Sin[(2*m + 1)*z] == Sum[(Subscript[B, 2*m + 1])^(2*n + 1)[q]* MathieuS[2*n + 1, q, z], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 28.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{(2m+2)z} = \sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\Mathieuse{2n+2}@{z}{q}}
\sin@@{(2m+2)z} = \sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\Mathieuse{2n+2}@{z}{q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin((2*m + 2)*z) = sum((B[2*m + 2])^(2*n + 2)(q)* MathieuSE(2*n + 2, q, z), n = 0..infinity)
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Sin[(2*m + 2)*z] == Sum[(Subscript[B, 2*m + 2])^(2*n + 2)[q]* MathieuS[2*n + 2, q, z], {n, 0, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |