View source for 28.14

{{DISPLAYTITLE:Mathieu Functions and Hill’s Equation - 28.14 Fourier Series}}

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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/28.14.E1 28.14.E1] || <math qid="Q8314">\Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Exp[I*(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.14.E2 28.14.E2] || <math qid="Q8315">\Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(nu, q, z) = sum((c[2*m])^(nu)(q)* cos((nu + 2*m)*z), m = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Cos[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.14.E3 28.14.E3] || <math qid="Q8316">\Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(nu, q, z) = sum((c[2*m])^(nu)(q)* sin((nu + 2*m)*z), m = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Sin[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.14.E4 28.14.E4] || <math qid="Q8317">qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0</syntaxhighlight> || <math>a = \Mathieueigvallambda{\nu}@{q}, c_{2m} = c_{2m}^{\nu}(q)</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*c[2*m + 2]-(a -(nu + 2*m)^(2))*c[2*m]+ q*c[2*m - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*Subscript[c, 2*m + 2]-(a -(\[Nu]+ 2*m)^(2))*Subscript[c, 2*m]+ q*Subscript[c, 2*m - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.14.E5 28.14.E5] || <math qid="Q8318">\sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(((c[2*m])^(nu)(q))^(2), m = - infinity..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[((Subscript[c, 2*m])^\[Nu][q])^(2), {m, - Infinity, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.14.E7 28.14.E7] || <math qid="Q8320">c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(c[- 2*m])^(- nu)(q) = (c[2*m])^(nu)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[c, - 2*m])^(- \[Nu])[q] == (Subscript[c, 2*m])^\[Nu][q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.14.E8 28.14.E8] || <math qid="Q8321">c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(c[2*m])^(nu)(- q) = (- 1)^(m)* (c[2*m])^(nu)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[c, 2*m])^\[Nu][- q] == (- 1)^(m)* (Subscript[c, 2*m])^\[Nu][q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.14#Ex1 28.14#Ex1] || <math qid="Q8322">c_{0}^{\nu}(0) = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0}^{\nu}(0) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(c[0])^(nu)(0) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[c, 0])^\[Nu][0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.14#Ex2 28.14#Ex2] || <math qid="Q8323">c_{2m}^{\nu}(0) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{2m}^{\nu}(0) = 0</syntaxhighlight> || <math>m \neq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(c[2*m])^(nu)(0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[c, 2*m])^\[Nu][0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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