View source for 28.5

{{DISPLAYTITLE:Mathieu Functions and Hill’s Equation - 28.5 Second Solutions <math>\Mathieufe{n}</math> , <math>\Mathieuge{n}</math>}}

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| [https://dlmf.nist.gov/28.5.E5 28.5.E5] || <math qid="Q8226">(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}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(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}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
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| [https://dlmf.nist.gov/28.5.E5 28.5.E5] || <math qid="Q8226">(S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} = \pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(S_{n}(q))^{2}\int_{0}^{2\pi}(g_{n}(x,q))^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(S[n](q))^(2)* int((g[n](x , q))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[S, n][q])^(2)* Integrate[(Subscript[g, n][x , q])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br><syntaxhighlight lang=mathematica>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}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
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| [https://dlmf.nist.gov/28.5#Ex1 28.5#Ex1] || <math qid="Q8227">C_{2m}(-q) = C_{2m}(q)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{2m}(-q) = C_{2m}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[2*m](- q) = C[2*m](q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 2*m][- q] == Subscript[C, 2*m][q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.5#Ex2 28.5#Ex2] || <math qid="Q8228">C_{2m+1}(-q) = S_{2m+1}(q)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{2m+1}(-q) = S_{2m+1}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[2*m + 1](- q) = S[2*m + 1](q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 2*m + 1][- q] == Subscript[S, 2*m + 1][q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/28.5#Ex3 28.5#Ex3] || <math qid="Q8229">S_{2m+2}(-q) = S_{2m+2}(q)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>S_{2m+2}(-q) = S_{2m+2}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">S[2*m + 2](- q) = S[2*m + 2](q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[S, 2*m + 2][- q] == Subscript[S, 2*m + 2][q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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