28.14: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/28.14.E1 28.14.E1] || [[Item:Q8314|<math>\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
| [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
|-  
|-  
| [https://dlmf.nist.gov/28.14.E2 28.14.E2] || [[Item:Q8315|<math>\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
| [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] || [[Item:Q8316|<math>\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
| [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
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/28.14.E4 28.14.E4] || [[Item:Q8317|<math>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 || - || -
| [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 || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/28.14.E5 28.14.E5] || [[Item:Q8318|<math>\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 || - || -
| [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 || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/28.14.E7 28.14.E7] || [[Item:Q8320|<math>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 || - || -
| [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 || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/28.14.E8 28.14.E8] || [[Item:Q8321|<math>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 || - || -
| [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 || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/28.14#Ex1 28.14#Ex1] || [[Item:Q8322|<math>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 || - || -
| [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 || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/28.14#Ex2 28.14#Ex2] || [[Item:Q8323|<math>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 || - || -
| [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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Latest revision as of 12:08, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
28.14.E1 me ν ⁡ ( z , q ) = ∑ m = - ∞ ∞ c 2 ⁢ m ν ⁢ ( q ) ⁢ e i ⁢ ( ν + 2 ⁢ m ) ⁢ z Mathieu-me 𝜈 𝑧 𝑞 superscript subscript 𝑚 subscript superscript 𝑐 𝜈 2 𝑚 𝑞 superscript 𝑒 imaginary-unit 𝜈 2 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(z,q\right)=\sum_{m=-\infty}% ^{\infty}c^{\nu}_{2m}(q)e^{\mathrm{i}(\nu+2m)z}}}
\Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}		 

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]
Missing Macro Error Failure - Skipped - Because timed out
28.14.E2 ce ν ⁡ ( z , q ) = ∑ m = - ∞ ∞ c 2 ⁢ m ν ⁢ ( q ) ⁢ cos ⁡ ( ν + 2 ⁢ m ) ⁢ z Mathieu-ce 𝜈 𝑧 𝑞 superscript subscript 𝑚 subscript superscript 𝑐 𝜈 2 𝑚 𝑞 𝜈 2 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{ce}_{\nu}\left(z,q\right)=\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}		 

MathieuCE(nu, q, z) = sum((c[2*m])^(nu)(q)* cos((nu + 2*m)*z), m = - infinity..infinity)

MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Cos[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]
Failure Failure Error Skipped - Because timed out
28.14.E3 se ν ⁡ ( z , q ) = ∑ m = - ∞ ∞ c 2 ⁢ m ν ⁢ ( q ) ⁢ sin ⁡ ( ν + 2 ⁢ m ) ⁢ z Mathieu-se 𝜈 𝑧 𝑞 superscript subscript 𝑚 subscript superscript 𝑐 𝜈 2 𝑚 𝑞 𝜈 2 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{se}_{\nu}\left(z,q\right)=\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}		 

MathieuSE(nu, q, z) = sum((c[2*m])^(nu)(q)* sin((nu + 2*m)*z), m = - infinity..infinity)

MathieuS[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Sin[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]
Failure Failure Error Skipped - Because timed out
28.14.E4 q ⁢ c 2 ⁢ m + 2 - ( a - ( ν + 2 ⁢ m ) 2 ) ⁢ c 2 ⁢ m + q ⁢ c 2 ⁢ m - 2 = 0 𝑞 subscript 𝑐 2 𝑚 2 𝑎 superscript 𝜈 2 𝑚 2 subscript 𝑐 2 𝑚 𝑞 subscript 𝑐 2 𝑚 2 0 {\displaystyle{\displaystyle qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2% m-2}=0}}
qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0		 a = λ ν ⁡ ( q ) , c 2 ⁢ m = c 2 ⁢ m ν ⁢ ( q ) formulae-sequence 𝑎 Mathieu-eigenvalue-lambda 𝜈 𝑞 subscript 𝑐 2 𝑚 superscript subscript 𝑐 2 𝑚 𝜈 𝑞 {\displaystyle{\displaystyle a=\lambda_{\nu}\left(q\right),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 ∑ m = - ∞ ∞ ( c 2 ⁢ m ν ⁢ ( q ) ) 2 = 1 superscript subscript 𝑚 superscript superscript subscript 𝑐 2 𝑚 𝜈 𝑞 2 1 {\displaystyle{\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		 

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 c - 2 ⁢ m - ν ⁢ ( q ) = c 2 ⁢ m ν ⁢ ( q ) superscript subscript 𝑐 2 𝑚 𝜈 𝑞 superscript subscript 𝑐 2 𝑚 𝜈 𝑞 {\displaystyle{\displaystyle c_{-2m}^{-\nu}(q)=c_{2m}^{\nu}(q)}}
c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)		 

(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 c 2 ⁢ m ν ⁢ ( - q ) = ( - 1 ) m ⁢ c 2 ⁢ m ν ⁢ ( q ) superscript subscript 𝑐 2 𝑚 𝜈 𝑞 superscript 1 𝑚 superscript subscript 𝑐 2 𝑚 𝜈 𝑞 {\displaystyle{\displaystyle c_{2m}^{\nu}(-q)=(-1)^{m}c_{2m}^{\nu}(q)}}
c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)		 

(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 c 0 ν ⁢ ( 0 ) = 1 superscript subscript 𝑐 0 𝜈 0 1 {\displaystyle{\displaystyle c_{0}^{\nu}(0)=1}}
c_{0}^{\nu}(0) = 1		 

(c[0])^(nu)(0) = 1
 
(Subscript[c, 0])^\[Nu][0] == 1
 Skipped - no semantic math Skipped - no semantic math - -
28.14#Ex2 c 2 ⁢ m ν ⁢ ( 0 ) = 0 superscript subscript 𝑐 2 𝑚 𝜈 0 0 {\displaystyle{\displaystyle c_{2m}^{\nu}(0)=0}}
c_{2m}^{\nu}(0) = 0		 m ≠ 0 𝑚 0 {\displaystyle{\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 - -
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