Mathieu Functions and Hill’s Equation - 28.14 Fourier Series
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}}
\Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
Sqrt[2]*MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Exp[I*(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]
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Missing Macro Error | Failure | - | Skipped - Because timed out |
| 28.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z}}
\Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | MathieuCE(nu, q, z) = sum((c[2*m])^(nu)(q)* cos((nu + 2*m)*z), m = - infinity..infinity)
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MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Cos[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]
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Failure | Failure | Error | Skipped - Because timed out |
| 28.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z}}
\Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | MathieuSE(nu, q, z) = sum((c[2*m])^(nu)(q)* sin((nu + 2*m)*z), m = - infinity..infinity)
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MathieuS[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Sin[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]
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Failure | Failure | Error | Skipped - Because timed out |
| 28.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0}
qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \Mathieueigvallambda{\nu}@{q}, c_{2m} = c_{2m}^{\nu}(q)} | q*c[2*m + 2]-(a -(nu + 2*m)^(2))*c[2*m]+ q*c[2*m - 2] = 0 |
q*Subscript[c, 2*m + 2]-(a -(\[Nu]+ 2*m)^(2))*Subscript[c, 2*m]+ q*Subscript[c, 2*m - 2] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2} = 1}
\sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(((c[2*m])^(nu)(q))^(2), m = - infinity..infinity) = 1 |
Sum[((Subscript[c, 2*m])^\[Nu][q])^(2), {m, - Infinity, Infinity}, GenerateConditions->None] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)}
c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (c[- 2*m])^(- nu)(q) = (c[2*m])^(nu)(q) |
(Subscript[c, - 2*m])^(- \[Nu])[q] == (Subscript[c, 2*m])^\[Nu][q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)}
c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (c[2*m])^(nu)(- q) = (- 1)^(m)* (c[2*m])^(nu)(q) |
(Subscript[c, 2*m])^\[Nu][- q] == (- 1)^(m)* (Subscript[c, 2*m])^\[Nu][q] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.14#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{0}^{\nu}(0) = 1}
c_{0}^{\nu}(0) = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (c[0])^(nu)(0) = 1 |
(Subscript[c, 0])^\[Nu][0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 28.14#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{2m}^{\nu}(0) = 0}
c_{2m}^{\nu}(0) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m \neq 0} | (c[2*m])^(nu)(0) = 0 |
(Subscript[c, 2*m])^\[Nu][0] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |