View source for 28.11

{{DISPLAYTITLE:Mathieu Functions and Hill’s Equation - 28.11 Expansions in Series of Mathieu Functions}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/28.11.E3 28.11.E3] || [[Item:Q8293|<math>1 = 2\sum_{n=0}^{\infty}A_{0}^{2n}(q)\Mathieuce{2n}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1 = 2\sum_{n=0}^{\infty}A_{0}^{2n}(q)\Mathieuce{2n}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1 = 2*sum((A[0])^(2*n)(q)* MathieuCE(2*n, q, z), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 == 2*Sum[(Subscript[A, 0])^(2*n)[q]* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.11.E4 28.11.E4] || [[Item:Q8294|<math>\cos@@{2mz} = \sum_{n=0}^{\infty}A_{2m}^{2n}(q)\Mathieuce{2n}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{2mz} = \sum_{n=0}^{\infty}A_{2m}^{2n}(q)\Mathieuce{2n}@{z}{q}</syntaxhighlight> || <math>m \neq 0</math> || <syntaxhighlight lang=mathematica>cos(2*m*z) = sum((A[2*m])^(2*n)(q)* MathieuCE(2*n, q, z), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[2*m*z] == Sum[(Subscript[A, 2*m])^(2*n)[q]* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.11.E5 28.11.E5] || [[Item:Q8295|<math>\cos@@{(2m+1)z} = \sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)\Mathieuce{2n+1}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@@{(2m+1)z} = \sum_{n=0}^{\infty}A_{2m+1}^{2n+1}(q)\Mathieuce{2n+1}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos((2*m + 1)*z) = sum((A[2*m + 1])^(2*n + 1)(q)* MathieuCE(2*n + 1, q, z), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.11.E6 28.11.E6] || [[Item:Q8296|<math>\sin@@{(2m+1)z} = \sum_{n=0}^{\infty}B_{2m+1}^{2n+1}(q)\Mathieuse{2n+1}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{(2m+1)z} = \sum_{n=0}^{\infty}B_{2m+1}^{2n+1}(q)\Mathieuse{2n+1}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin((2*m + 1)*z) = sum((B[2*m + 1])^(2*n + 1)(q)* MathieuSE(2*n + 1, q, z), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.11.E7 28.11.E7] || [[Item:Q8297|<math>\sin@@{(2m+2)z} = \sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\Mathieuse{2n+2}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{(2m+2)z} = \sum_{n=0}^{\infty}B_{2m+2}^{2n+2}(q)\Mathieuse{2n+2}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin((2*m + 2)*z) = sum((B[2*m + 2])^(2*n + 2)(q)* MathieuSE(2*n + 2, q, z), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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