Results of Mathieu Functions and Hill’s Equation: Difference between revisions

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Notation: 28.1 Special Notation
Mathieu Functions of Integer Order: 28.2 Definitions and Basic Properties
28.3 Graphics
28.4 Fourier Series
28.5 Second Solutions Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieufe{n}} , Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieuge{n}}
28.6 Expansions for Small Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
28.7 Analytic Continuation of Eigenvalues
28.8 Asymptotic Expansions for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
28.9 Zeros
28.10 Integral Equations
28.11 Expansions in Series of Mathieu Functions
Mathieu Functions of Noninteger Order: 28.12 Definitions and Basic Properties
28.13 Graphics
28.14 Fourier Series
28.15 Expansions for Small Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
28.16 Asymptotic Expansions for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
28.17 Stability as Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x\to\pm\infty}
28.18 Integrals and Integral Equations
28.19 Expansions in Series of Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Mathieume{\nu+2n}} Functions
Modified Mathieu Functions: 28.20 Definitions and Basic Properties
28.21 Graphics
28.22 Connection Formulas
28.23 Expansions in Series of Bessel Functions
28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions
28.25 Asymptotic Expansions for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{z}}
28.26 Asymptotic Approximations for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
28.27 Addition Theorems
28.28 Integrals, Integral Representations, and Integral Equations
Hill’s Equation: 28.29 Definitions and Basic Properties
28.30 Expansions in Series of Eigenfunctions
28.31 Equations of Whittaker–Hill and Ince
Applications: 28.32 Mathematical Applications
28.33 Physical Applications
Computation: 28.34 Methods of Computation
28.35 Tables
28.36 Software

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+<div style="-moz-column-count:2; column-count:2;">
-{| class="wikitable sortable" style="margin: 0;"
+; Notation : [[28.1|28.1 Special Notation]]<br>
-|-
+; Mathieu Functions of Integer Order : [[28.2|28.2 Definitions and Basic Properties]]<br>[[28.3|28.3 Graphics]]<br>[[28.4|28.4 Fourier Series]]<br>[[28.5|28.5 Second Solutions <math>\Mathieufe{n}</math> , <math>\Mathieuge{n}</math>]]<br>[[28.6|28.6 Expansions for Small <math>q</math>]]<br>[[28.7|28.7 Analytic Continuation of Eigenvalues]]<br>[[28.8|28.8 Asymptotic Expansions for Large <math>q</math>]]<br>[[28.9|28.9 Zeros]]<br>[[28.10|28.10 Integral Equations]]<br>[[28.11|28.11 Expansions in Series of Mathieu Functions]]<br>
-! scope="col" style="position: sticky; top: 0;" | DLMF
+; Mathieu Functions of Noninteger Order : [[28.12|28.12 Definitions and Basic Properties]]<br>[[28.13|28.13 Graphics]]<br>[[28.14|28.14 Fourier Series]]<br>[[28.15|28.15 Expansions for Small <math>q</math>]]<br>[[28.16|28.16 Asymptotic Expansions for Large <math>q</math>]]<br>[[28.17|28.17 Stability as <math>x\to\pm\infty</math>]]<br>[[28.18|28.18 Integrals and Integral Equations]]<br>[[28.19|28.19 Expansions in Series of <math>\Mathieume{\nu+2n}</math> Functions]]<br>
-! scope="col" style="position: sticky; top: 0;" | Formula
+; Modified Mathieu Functions : [[28.20|28.20 Definitions and Basic Properties]]<br>[[28.21|28.21 Graphics]]<br>[[28.22|28.22 Connection Formulas]]<br>[[28.23|28.23 Expansions in Series of Bessel Functions]]<br>[[28.24|28.24 Expansions in Series of Cross-Products of Bessel Functions or
-! scope="col" style="position: sticky; top: 0;" | Constraints
+Modified Bessel Functions]]<br>[[28.25|28.25 Asymptotic Expansions for Large <math>\realpart@@{z}</math>]]<br>[[28.26|28.26 Asymptotic Approximations for Large <math>q</math>]]<br>[[28.27|28.27 Addition Theorems]]<br>[[28.28|28.28 Integrals, Integral Representations, and Integral Equations]]<br>
-! scope="col" style="position: sticky; top: 0;" | Maple
+; Hill’s Equation : [[28.29|28.29 Definitions and Basic Properties]]<br>[[28.30|28.30 Expansions in Series of Eigenfunctions]]<br>[[28.31|28.31 Equations of Whittaker–Hill and Ince]]<br>
-! scope="col" style="position: sticky; top: 0;" | Mathematica
+; Applications : [[28.32|28.32 Mathematical Applications]]<br>[[28.33|28.33 Physical Applications]]<br>
-! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
+; Computation : [[28.34|28.34 Methods of Computation]]<br>[[28.35|28.35 Tables]]<br>[[28.36|28.36 Software]]<br>
-! 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
-|-
-| [https://dlmf.nist.gov/28.1#Ex15 28.1#Ex15] || [[Item:Q8138|<math>\mathrm{Se}_{n}(s,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{Se}_{n}(s,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>S*exp(1)[n]*(s , z) = (MathieuCE(n, q, z))/(MathieuCE(n, q, 0))</syntaxhighlight> || <syntaxhighlight lang=mathematica>S*Subscript[E, n]*(s , z) == Divide[MathieuC[n, q, z],MathieuC[n, q, 0]]</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.1#Ex16 28.1#Ex16] || [[Item:Q8139|<math>\mathrm{So}_{n}(s,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{So}_{n}(s,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>So[n](s , z) = (MathieuSE(n, q, z))/(diff( MathieuSE(n, q, 0), 0$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[So, n][s , z] == Divide[MathieuS[n, q, z],D[MathieuS[n, q, 0], {0, 1}]]</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/28.1#Ex17 28.1#Ex17] || [[Item:Q8140|<math>\mathrm{Se}_{n}(c,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{Se}_{n}(c,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>S*exp(1)[n]*(c , z) = (MathieuCE(n, q, z))/(MathieuCE(n, q, 0))</syntaxhighlight> || <syntaxhighlight lang=mathematica>S*Subscript[E, n]*(c , z) == Divide[MathieuC[n, q, z],MathieuC[n, q, 0]]</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.1#Ex18 28.1#Ex18] || [[Item:Q8141|<math>\mathrm{So}_{n}(c,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mathrm{So}_{n}(c,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>So[n](c , z) = (MathieuSE(n, q, z))/(diff( MathieuSE(n, q, 0), 0$(1) ))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[So, n][c , z] == Divide[MathieuS[n, q, z],D[MathieuS[n, q, 0], {0, 1}]]</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/28.2.E14 28.2.E14] || [[Item:Q8157|<math>w(z+\pi) = e^{\pi\iunit\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi) = e^{\pi\iunit\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi) = exp(Pi*I*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi] == Exp[Pi*I*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.389122976+2.558671223*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.732824151+2.239220255*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.3891229743891893, 2.5586712226918134]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.163689701656905, 2.469736091084983]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E17 28.2.E17] || [[Item:Q8160|<math>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi)+ w(z - Pi) = 2*cos(Pi*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi]+ w[z - Pi] == 2*Cos[Pi*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.661616693+6.639028674*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.639028674+1.661616692*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.6616166873386105, 6.63902867151764]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[14.098728614058, -5.830503683799378]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E18 28.2.E18] || [[Item:Q8161|<math>w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z) = sum(c[2*n]*exp(I*(nu + 2*n)*z), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z] == Sum[Subscript[c, 2*n]*Exp[I*(\[Nu]+ 2*n)*z], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.2.E19 28.2.E19] || [[Item:Q8162|<math>qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*c[2*n + 2]-(a -(nu + 2*n)^(2))*c[2*n]+ q*c[2*n - 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*n + 2]-(a -(\[Nu]+ 2*n)^(2))*Subscript[c, 2*n]+ q*Subscript[c, 2*n - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.2.E20 28.2.E20] || [[Item:Q8163|<math>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((abs(c[2*n]))^(1/abs(n)), n = + infinity) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Abs[Subscript[c, 2*n]])^(1/Abs[n]), n -> + Infinity, GenerateConditions->None] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.2.E23 28.2.E23] || [[Item:Q8166|<math>\Mathieueigvala{n}@{0} = n^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/28.2.E24 28.2.E24] || [[Item:Q8167|<math>\Mathieueigvalb{n}@{0} = n^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/28.2.E26 28.2.E26] || [[Item:Q8169|<math>\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n, - q) = MathieuA(2*n, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n, - q] == MathieuCharacteristicA[2*n, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
-|-
-| [https://dlmf.nist.gov/28.2.E27 28.2.E27] || [[Item:Q8170|<math>\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n + 1, - q) = MathieuB(2*n + 1, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n + 1, - q] == MathieuCharacteristicB[2*n + 1, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
-|-
-| [https://dlmf.nist.gov/28.2.E28 28.2.E28] || [[Item:Q8171|<math>\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(2*n + 2, - q) = MathieuB(2*n + 2, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[2*n + 2, - q] == MathieuCharacteristicB[2*n + 2, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
-|-
-| [https://dlmf.nist.gov/28.2#Ex4 28.2#Ex4] || [[Item:Q8172|<math>\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(0, 0, z) = 1/(sqrt(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[0, 0, z] == 1/(Sqrt[2])</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/28.2#Ex5 28.2#Ex5] || [[Item:Q8173|<math>\Mathieuce{n}@{z}{0} = \cos@{nz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{n}@{z}{0} = \cos@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(n, 0, z) = cos(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[n, 0, z] == Cos[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6753267742469401, 0.4379310296367226]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.1123802552186532, 0.12519411502047795]
-Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2#Ex6 28.2#Ex6] || [[Item:Q8174|<math>\Mathieuse{n}@{z}{0} = \sin@{nz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{n}@{z}{0} = \sin@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(n, 0, z) = sin(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[n, 0, z] == Sin[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.17898073764673827, 1.8916506821927568]
-Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[4.947243351054952, 0.9068272427732345]
-Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2#Ex7 28.2#Ex7] || [[Item:Q8175|<math>\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuCE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[6.9214963829238805, 34.195194735367046]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.5092269783308243, -0.4627812517943034]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2#Ex8 28.2#Ex8] || [[Item:Q8176|<math>\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuSE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.15495486e-1+.3109277201e-1*I
-Test Values: {q = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.592260336+2.720760990*I
-Test Values: {q = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-11.13627493115099, -34.66471446201499]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-4.303849824281496, -4.82944497847242]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E31 28.2.E31] || [[Item:Q8177|<math>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuCE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuC[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.2.E32 28.2.E32] || [[Item:Q8178|<math>\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuSE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuS[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.2.E33 28.2.E33] || [[Item:Q8179|<math>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.2.E34 28.2.E34] || [[Item:Q8180|<math>\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n, - q, z) = (- 1)^(n)* MathieuCE(2*n, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n, - q, z] == (- 1)^(n)* MathieuC[2*n, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.40308591506050084, 0.46785287118948815]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.60084404002985, 1.182666432116677]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E35 28.2.E35] || [[Item:Q8181|<math>\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n + 1, - q, z) = (- 1)^(n)* MathieuSE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n + 1, - q, z] == (- 1)^(n)* MathieuS[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.5024747894079764, -2.6392504264802374]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.189026591129222, 0.3274807845663039]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E36 28.2.E36] || [[Item:Q8182|<math>\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 1, - q, z) = (- 1)^(n)* MathieuCE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 1, - q, z] == (- 1)^(n)* MathieuC[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.280260494012772, -3.1853558239364403]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.634104542197209, -1.1703184896606507]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.2.E37 28.2.E37] || [[Item:Q8183|<math>\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 2, - q, z) = (- 1)^(n)* MathieuSE(2*n + 2, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 2, - q, z] == (- 1)^(n)* MathieuS[2*n + 2, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3430671662+7.821986266*I
-Test Values: {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 20.99712460-1.294028748*I
-Test Values: {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.02456715747845, -1.021331524922309]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.169415024309792, -3.4466753320968735]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.4.E1 28.4.E1] || [[Item:Q8186|<math>\Mathieuce{2n}@{z}{q} = \sum_{m=0}^{\infty}A^{2n}_{2m}(q)\cos@@{2mz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n}@{z}{q} = \sum_{m=0}^{\infty}A^{2n}_{2m}(q)\cos@@{2mz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n, q, z) = sum((A[2*m])^(2*n)(q)* cos(2*m*z), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n, q, z] == Sum[(Subscript[A, 2*m])^(2*n)[q]* Cos[2*m*z], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.4.E2 28.4.E2] || [[Item:Q8187|<math>\Mathieuce{2n+1}@{z}{q} = \sum_{m=0}^{\infty}A^{2n+1}_{2m+1}(q)\cos@@{(2m+1)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n+1}@{z}{q} = \sum_{m=0}^{\infty}A^{2n+1}_{2m+1}(q)\cos@@{(2m+1)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n + 1, q, z) = sum((A[2*m + 1])^(2*n + 1)(q)* cos((2*m + 1)*z), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n + 1, q, z] == Sum[(Subscript[A, 2*m + 1])^(2*n + 1)[q]* Cos[(2*m + 1)*z], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.4.E3 28.4.E3] || [[Item:Q8188|<math>\Mathieuse{2n+1}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+1}_{2m+1}(q)\sin@@{(2m+1)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+1}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+1}_{2m+1}(q)\sin@@{(2m+1)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 1, q, z) = sum((B[2*m + 1])^(2*n + 1)(q)* sin((2*m + 1)*z), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 1, q, z] == Sum[(Subscript[B, 2*m + 1])^(2*n + 1)[q]* Sin[(2*m + 1)*z], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.4.E4 28.4.E4] || [[Item:Q8189|<math>\Mathieuse{2n+2}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+2}_{2m+2}(q)\sin@@{(2m+2)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+2}@{z}{q} = \sum_{m=0}^{\infty}B^{2n+2}_{2m+2}(q)\sin@@{(2m+2)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 2, q, z) = sum((B[2*m + 2])^(2*n + 2)(q)* sin((2*m + 2)*z), m = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 2, q, z] == Sum[(Subscript[B, 2*m + 2])^(2*n + 2)[q]* Sin[(2*m + 2)*z], {m, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex1 28.4#Ex1] || [[Item:Q8190|<math>aA_{0}-qA_{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>aA_{0}-qA_{2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a*A[0]- q*A[2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a*Subscript[A, 0]- q*Subscript[A, 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex2 28.4#Ex2] || [[Item:Q8191|<math>(a-4)A_{2}-q(2A_{0}+A_{4}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-4)A_{2}-q(2A_{0}+A_{4}) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4)*A[2]- q*(2*A[0]+ A[4]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4)*Subscript[A, 2]- q*(2*Subscript[A, 0]+ Subscript[A, 4]) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex3 28.4#Ex3] || [[Item:Q8192|<math>(a-4m^{2})A_{2m}-q(A_{2m-2}+A_{2m+2}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-4m^{2})A_{2m}-q(A_{2m-2}+A_{2m+2}) = 0</syntaxhighlight> || <math>a = \Mathieueigvala{2n}@{q}, A_{2m} = A_{2m}^{2n}(q)</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4*(m)^(2))*A[2*m]- q*(A[2*m - 2]+ A[2*m + 2]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4*(m)^(2))*Subscript[A, 2*m]- q*(Subscript[A, 2*m - 2]+ Subscript[A, 2*m + 2]) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex4 28.4#Ex4] || [[Item:Q8193|<math>(a-1-q)A_{1}-qA_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-1-q)A_{1}-qA_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 1 - q)*A[1]- q*A[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 1 - q)*Subscript[A, 1]- q*Subscript[A, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex5 28.4#Ex5] || [[Item:Q8194|<math>\left(a-(2m+1)^{2}\right)A_{2m+1}-q(A_{2m-1}+A_{2m+3}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(a-(2m+1)^{2}\right)A_{2m+1}-q(A_{2m-1}+A_{2m+3}) = 0</syntaxhighlight> || <math>a = \Mathieueigvala{2n+1}@{q}, A_{2m+1} = A_{2m+1}^{2n+1}(q)</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a -(2*m + 1)^(2))*A[2*m + 1]- q*(A[2*m - 1]+ A[2*m + 3]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a -(2*m + 1)^(2))*Subscript[A, 2*m + 1]- q*(Subscript[A, 2*m - 1]+ Subscript[A, 2*m + 3]) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex6 28.4#Ex6] || [[Item:Q8195|<math>(a-1+q)B_{1}-qB_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-1+q)B_{1}-qB_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 1 + q)*B[1]- q*B[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 1 + q)*Subscript[B, 1]- q*Subscript[B, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex7 28.4#Ex7] || [[Item:Q8196|<math>\left(a-(2m+1)^{2}\right)B_{2m+1}-q(B_{2m-1}+B_{2m+3}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(a-(2m+1)^{2}\right)B_{2m+1}-q(B_{2m-1}+B_{2m+3}) = 0</syntaxhighlight> || <math>a = \Mathieueigvalb{2n+1}@{q}, B_{2m+1} = B_{2m+1}^{2n+1}(q)</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a -(2*m + 1)^(2))*B[2*m + 1]- q*(B[2*m - 1]+ B[2*m + 3]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a -(2*m + 1)^(2))*Subscript[B, 2*m + 1]- q*(Subscript[B, 2*m - 1]+ Subscript[B, 2*m + 3]) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex8 28.4#Ex8] || [[Item:Q8197|<math>(a-4)B_{2}-qB_{4} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-4)B_{2}-qB_{4} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4)*B[2]- q*B[4] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4)*Subscript[B, 2]- q*Subscript[B, 4] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex9 28.4#Ex9] || [[Item:Q8198|<math>(a-4m^{2})B_{2m}-q(B_{2m-2}+B_{2m+2}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-4m^{2})B_{2m}-q(B_{2m-2}+B_{2m+2}) = 0</syntaxhighlight> || <math>a = \Mathieueigvalb{2n+2}@{q}, B_{2m+2} = B_{2m+2}^{2n+2}(q).</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4*(m)^(2))*B[2*m]- q*(B[2*m - 2]+ B[2*m + 2]) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - 4*(m)^(2))*Subscript[B, 2*m]- q*(Subscript[B, 2*m - 2]+ Subscript[B, 2*m + 2]) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E9 28.4.E9] || [[Item:Q8199|<math>2\left(A^{2n}_{0}(q)\right)^{2}+\sum_{m=1}^{\infty}\left(A^{2n}_{2m}(q)\right)^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2\left(A^{2n}_{0}(q)\right)^{2}+\sum_{m=1}^{\infty}\left(A^{2n}_{2m}(q)\right)^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*((A[0])^(2*n)(q))^(2)+ sum(((A[2*m])^(2*n)(q))^(2), m = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*((Subscript[A, 0])^(2*n)[q])^(2)+ Sum[((Subscript[A, 2*m])^(2*n)[q])^(2), {m, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E10 28.4.E10] || [[Item:Q8200|<math>\sum_{m=0}^{\infty}\left(A^{2n+1}_{2m+1}(q)\right)^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{m=0}^{\infty}\left(A^{2n+1}_{2m+1}(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(((A[2*m + 1])^(2*n + 1)(q))^(2), m = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[((Subscript[A, 2*m + 1])^(2*n + 1)[q])^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E11 28.4.E11] || [[Item:Q8201|<math>\sum_{m=0}^{\infty}\left(B^{2n+1}_{2m+1}(q)\right)^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{m=0}^{\infty}\left(B^{2n+1}_{2m+1}(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(((B[2*m + 1])^(2*n + 1)(q))^(2), m = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[((Subscript[B, 2*m + 1])^(2*n + 1)[q])^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E12 28.4.E12] || [[Item:Q8202|<math>\sum_{m=0}^{\infty}\left(B^{2n+2}_{2m+2}(q)\right)^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{m=0}^{\infty}\left(B^{2n+2}_{2m+2}(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(((B[2*m + 2])^(2*n + 2)(q))^(2), m = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[((Subscript[B, 2*m + 2])^(2*n + 2)[q])^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex10 28.4#Ex10] || [[Item:Q8203|<math>A^{0}_{0}(0) = 1/\sqrt{2},\quad A^{2n}_{2n}(0)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{0}_{0}(0) = 1/\sqrt{2},\quad A^{2n}_{2n}(0)</syntaxhighlight> || <math>n > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[0])^(0)(0) = 1/(sqrt(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 0])^(0)[0] == 1/(Sqrt[2])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex11 28.4#Ex11] || [[Item:Q8204|<math>A^{2n}_{2m}(0) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{2n}_{2m}(0) = 0</syntaxhighlight> || <math>n \neq m</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2*m])^(2*n)(0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2*m])^(2*n)[0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex12 28.4#Ex12] || [[Item:Q8205|<math>A^{2n+1}_{2n+1}(0) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{2n+1}_{2n+1}(0) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2*n + 1])^(2*n + 1)(0) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2*n + 1])^(2*n + 1)[0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex13 28.4#Ex13] || [[Item:Q8206|<math>A^{2n+1}_{2m+1}(0) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{2n+1}_{2m+1}(0) = 0</syntaxhighlight> || <math>n \neq m</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2*m + 1])^(2*n + 1)(0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2*m + 1])^(2*n + 1)[0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex14 28.4#Ex14] || [[Item:Q8207|<math>B^{2n+1}_{2n+1}(0) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+1}_{2n+1}(0) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*n + 1])^(2*n + 1)(0) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*n + 1])^(2*n + 1)[0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex15 28.4#Ex15] || [[Item:Q8208|<math>B^{2n+1}_{2m+1}(0) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+1}_{2m+1}(0) = 0</syntaxhighlight> || <math>n \neq m</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*m + 1])^(2*n + 1)(0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*m + 1])^(2*n + 1)[0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex16 28.4#Ex16] || [[Item:Q8209|<math>B^{2n+2}_{2n+2}(0) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+2}_{2n+2}(0) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*n + 2])^(2*n + 2)(0) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*n + 2])^(2*n + 2)[0] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4#Ex17 28.4#Ex17] || [[Item:Q8210|<math>B^{2n+2}_{2m+2}(0) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+2}_{2m+2}(0) = 0</syntaxhighlight> || <math>n \neq m</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*m + 2])^(2*n + 2)(0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*m + 2])^(2*n + 2)[0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E17 28.4.E17] || [[Item:Q8211|<math>A^{2n}_{2m}(-q) = (-1)^{n-m}A^{2n}_{2m}(q)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{2n}_{2m}(-q) = (-1)^{n-m}A^{2n}_{2m}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2*m])^(2*n)(- q) = (- 1)^(n - m)* (A[2*m])^(2*n)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2*m])^(2*n)[- q] == (- 1)^(n - m)* (Subscript[A, 2*m])^(2*n)[q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E18 28.4.E18] || [[Item:Q8212|<math>B^{2n+2}_{2m+2}(-q) = (-1)^{n-m}B^{2n+2}_{2m+2}(q)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+2}_{2m+2}(-q) = (-1)^{n-m}B^{2n+2}_{2m+2}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*m + 2])^(2*n + 2)(- q) = (- 1)^(n - m)* (B[2*m + 2])^(2*n + 2)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*m + 2])^(2*n + 2)[- q] == (- 1)^(n - m)* (Subscript[B, 2*m + 2])^(2*n + 2)[q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E19 28.4.E19] || [[Item:Q8213|<math>A^{2n+1}_{2m+1}(-q) = (-1)^{n-m}B^{2n+1}_{2m+1}(q)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A^{2n+1}_{2m+1}(-q) = (-1)^{n-m}B^{2n+1}_{2m+1}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A[2*m + 1])^(2*n + 1)(- q) = (- 1)^(n - m)* (B[2*m + 1])^(2*n + 1)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[A, 2*m + 1])^(2*n + 1)[- q] == (- 1)^(n - m)* (Subscript[B, 2*m + 1])^(2*n + 1)[q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.4.E20 28.4.E20] || [[Item:Q8214|<math>B^{2n+1}_{2m+1}(-q) = (-1)^{n-m}A^{2n+1}_{2m+1}(q)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B^{2n+1}_{2m+1}(-q) = (-1)^{n-m}A^{2n+1}_{2m+1}(q)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2*m + 1])^(2*n + 1)(- q) = (- 1)^(n - m)* (A[2*m + 1])^(2*n + 1)(q)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2*m + 1])^(2*n + 1)[- q] == (- 1)^(n - m)* (Subscript[A, 2*m + 1])^(2*n + 1)[q]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.5.E5 28.5.E5] || [[Item:Q8226|<math>(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
-|-
-| [https://dlmf.nist.gov/28.5.E5 28.5.E5] || [[Item:Q8226|<math>(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
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.5#Ex1 28.5#Ex1] || [[Item:Q8227|<math>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 || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.5#Ex2 28.5#Ex2] || [[Item:Q8228|<math>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 || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.5#Ex3 28.5#Ex3] || [[Item:Q8229|<math>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 || - || -
-|-
-| [https://dlmf.nist.gov/28.6.E20 28.6.E20] || [[Item:Q8254|<math>\liminf_{n\to\infty}\frac{\rho_{n}^{(j)}}{n^{2}} \geq kk^{\prime}(\compellintKk@{k})^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\liminf_{n\to\infty}\frac{\rho_{n}^{(j)}}{n^{2}} \geq kk^{\prime}(\compellintKk@{k})^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>[n = infinity]*((rho[n])^(j))/((n)^(2)) >= k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[, n -> Infinity]*Divide[(Subscript[\[Rho], n])^(j),(n)^(2)] >= k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: GreaterEqual[Complex[0.5000000000000001, 0.8660254037844386], Indeterminate]
-Test Values: {Rule[j, 1], Rule[k, 1], Rule[n, 1], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ρ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: GreaterEqual[Complex[0.12500000000000003, 0.21650635094610965], Indeterminate]
-Test Values: {Rule[j, 1], Rule[k, 1], Rule[n, 2], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ρ, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.6.E20 28.6.E20] || [[Item:Q8254|<math>kk^{\prime}(\compellintKk@{k})^{2} = 2.04183\;4\dots</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>kk^{\prime}(\compellintKk@{k})^{2} = 2.04183\;4\dots</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2) = 2.041834</syntaxhighlight> || <syntaxhighlight lang=mathematica>k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2) == 2.041834</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[k, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[4.25477173820126, -1.5664714954570549]
-Test Values: {Rule[k, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.7.E1 28.7.E1] || [[Item:Q8261|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.7.E2 28.7.E2] || [[Item:Q8262|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.7.E3 28.7.E3] || [[Item:Q8263|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.7.E4 28.7.E4] || [[Item:Q8264|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.8#Ex3 28.8#Ex3] || [[Item:Q8273|<math>\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) = ((2)^(m -((1)/(2))))/(sigma[m])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))+ (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Sigma], m]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])+ (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.8#Ex4 28.8#Ex4] || [[Item:Q8274|<math>\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) = ((2)^(m -((1)/(2))))/(tau[m + 1])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))- (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Tau], m + 1]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])- (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E1 28.10.E1] || [[Item:Q8280|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(cos(2*h*cos(z)*cos(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2)) = ((A[0])^(2*n)((h)^(2)))/(MathieuCE(2*n, (h)^(2), (1)/(2)*Pi))*MathieuCE(2*n, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Cos[2*h*Cos[z]*Cos[t]]*MathieuC[2*n, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[A, 0])^(2*n)[(h)^(2)],MathieuC[2*n, (h)^(2), Divide[1,2]*Pi]]*MathieuC[2*n, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E2 28.10.E2] || [[Item:Q8281|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{0}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n}@{t}{h^{2}}\diff{t} = \frac{A_{0}^{2n}(h^{2})}{\Mathieuce{2n}@{0}{h^{2}}}\Mathieuce{2n}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(cosh(2*h*sin(z)*sin(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2)) = ((A[0])^(2*n)((h)^(2)))/(MathieuCE(2*n, (h)^(2), 0))*MathieuCE(2*n, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Cosh[2*h*Sin[z]*Sin[t]]*MathieuC[2*n, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[A, 0])^(2*n)[(h)^(2)],MathieuC[2*n, (h)^(2), 0]]*MathieuC[2*n, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E3 28.10.E3] || [[Item:Q8282|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = -\frac{hA_{1}^{2n+1}(h^{2})}{\Mathieuce{2n+1}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = -\frac{hA_{1}^{2n+1}(h^{2})}{\Mathieuce{2n+1}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(sin(2*h*cos(z)*cos(t))*MathieuCE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) = -((hA[1])^(2*n + 1)((h)^(2)))/(subs( temp=(1)/(2)*Pi, diff( MathieuCE(2*n + 1, (h)^(2), temp), temp$(1) ) ))*MathieuCE(2*n + 1, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Sin[2*h*Cos[z]*Cos[t]]*MathieuC[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == -Divide[(Subscript[hA, 1])^(2*n + 1)[(h)^(2)],D[MathieuC[2*n + 1, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi]*MathieuC[2*n + 1, (h)^(2), z]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E4 28.10.E4] || [[Item:Q8283|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = \frac{A_{1}^{2n+1}(h^{2})}{2\Mathieuce{2n+1}@{0}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\cosh@{2h\sin@@{z}\sin@@{t}}\Mathieuce{2n+1}@{t}{h^{2}}\diff{t} = \frac{A_{1}^{2n+1}(h^{2})}{2\Mathieuce{2n+1}@{0}{h^{2}}}\Mathieuce{2n+1}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(cos(z)*cos(t)*cosh(2*h*sin(z)*sin(t))*MathieuCE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) = ((A[1])^(2*n + 1)((h)^(2)))/(2*MathieuCE(2*n + 1, (h)^(2), 0))*MathieuCE(2*n + 1, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Cos[z]*Cos[t]*Cosh[2*h*Sin[z]*Sin[t]]*MathieuC[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[A, 1])^(2*n + 1)[(h)^(2)],2*MathieuC[2*n + 1, (h)^(2), 0]]*MathieuC[2*n + 1, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E5 28.10.E5] || [[Item:Q8284|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{hB_{1}^{2n+1}(h^{2})}{\Mathieuse{2n+1}'@{0}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{hB_{1}^{2n+1}(h^{2})}{\Mathieuse{2n+1}'@{0}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(sinh(2*h*sin(z)*sin(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) = ((hB[1])^(2*n + 1)((h)^(2)))/(subs( temp=0, diff( MathieuSE(2*n + 1, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 1, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Sinh[2*h*Sin[z]*Sin[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[hB, 1])^(2*n + 1)[(h)^(2)],D[MathieuS[2*n + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0]*MathieuS[2*n + 1, (h)^(2), z]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E6 28.10.E6] || [[Item:Q8285|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{B_{1}^{2n+1}(h^{2})}{2\Mathieuse{2n+1}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{B_{1}^{2n+1}(h^{2})}{2\Mathieuse{2n+1}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(sin(z)*sin(t)*cos(2*h*cos(z)*cos(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) = ((B[1])^(2*n + 1)((h)^(2)))/(2*MathieuSE(2*n + 1, (h)^(2), (1)/(2)*Pi))*MathieuSE(2*n + 1, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Sin[z]*Sin[t]*Cos[2*h*Cos[z]*Cos[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[B, 1])^(2*n + 1)[(h)^(2)],2*MathieuS[2*n + 1, (h)^(2), Divide[1,2]*Pi]]*MathieuS[2*n + 1, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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-| [https://dlmf.nist.gov/28.10.E7 28.10.E7] || [[Item:Q8286|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = -\frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = -\frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(sin(z)*sin(t)*sin(2*h*cos(z)*cos(t))*MathieuSE(2*n + 2, (h)^(2), t), t = 0..(Pi)/(2)) = -((hB[2])^(2*n + 2)((h)^(2)))/(2*subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*n + 2, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 2, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Sin[z]*Sin[t]*Sin[2*h*Cos[z]*Cos[t]]*MathieuS[2*n + 2, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == -Divide[(Subscript[hB, 2])^(2*n + 2)[(h)^(2)],2*(D[MathieuS[2*n + 2, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi)]*MathieuS[2*n + 2, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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-| [https://dlmf.nist.gov/28.10.E8 28.10.E8] || [[Item:Q8287|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = \frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{0}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\cos@@{z}\cos@@{t}\sinh@{2h\sin@@{z}\sin@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = \frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{0}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2)/(Pi)*int(cos(z)*cos(t)*sinh(2*h*sin(z)*sin(t))*MathieuSE(2*n + 2, (h)^(2), t), t = 0..(Pi)/(2)) = ((hB[2])^(2*n + 2)((h)^(2)))/(2*subs( temp=0, diff( MathieuSE(2*n + 2, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 2, (h)^(2), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2,Pi]*Integrate[Cos[z]*Cos[t]*Sinh[2*h*Sin[z]*Sin[t]]*MathieuS[2*n + 2, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] == Divide[(Subscript[hB, 2])^(2*n + 2)[(h)^(2)],2*(D[MathieuS[2*n + 2, (h)^(2), temp], {temp, 1}]/.temp-> 0)]*MathieuS[2*n + 2, (h)^(2), z]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [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
-|-
-| [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
-|-
-| [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
-|-
-| [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
-|-
-| [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
-|-
-| [https://dlmf.nist.gov/28.12.E4 28.12.E4] || [[Item:Q8301|<math>\Mathieume{\nu}@{z}{0} = e^{\iunit\nu z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{\nu}@{z}{0} = e^{\iunit\nu z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[\[Nu], 0, z] == Exp[I*\[Nu]*z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9861942690160291, -0.9067989679250835]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.7892990057566478, 0.4620307840711049]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E5 28.12.E5] || [[Item:Q8302|<math>\int_{0}^{\pi}\Mathieume{\nu}@{x}{q}\Mathieume{\nu}@{-x}{q}\diff{x} = \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\pi}\Mathieume{\nu}@{x}{q}\Mathieume{\nu}@{-x}{q}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Sqrt[2]*MathieuC[\[Nu], q, x]*Sqrt[2]*MathieuC[\[Nu], q, - x], {x, 0, Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.12.E6 28.12.E6] || [[Item:Q8303|<math>\Mathieume{\nu}@{z+\pi}{q} = e^{\pi\iunit\nu}\Mathieume{\nu}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{\nu}@{z+\pi}{q} = e^{\pi\iunit\nu}\Mathieume{\nu}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[\[Nu], q, z + Pi] == Exp[Pi*I*\[Nu]]*Sqrt[2]*MathieuC[\[Nu], q, z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-6.370347292395534, -6.192387567232969]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[33.312348543319324, -34.35988503520594]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E7 28.12.E7] || [[Item:Q8304|<math>\int_{0}^{\pi}\Mathieume{\nu+2m}@{x}{q}\Mathieume{\nu+2n}@{-x}{q}\diff{x} = 0,</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\pi}\Mathieume{\nu+2m}@{x}{q}\Mathieume{\nu+2n}@{-x}{q}\diff{x} = 0,</syntaxhighlight> || <math>m \neq n</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Sqrt[2]*MathieuC[\[Nu]+ 2*m, q, x]*Sqrt[2]*MathieuC[\[Nu]+ 2*n, q, - x], {x, 0, Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Skipped - Unable to analyze test case: Null || Skipped - Unable to analyze test case: Null || - || -
-|-
-| [https://dlmf.nist.gov/28.12.E8 28.12.E8] || [[Item:Q8305|<math>\Mathieume{-\nu}@{z}{q} = \Mathieume{\nu}@{-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{-\nu}@{z}{q} = \Mathieume{\nu}@{-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[- \[Nu], q, z] == Sqrt[2]*MathieuC[\[Nu], q, - z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.065655571425399, 0.7817797951498487]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.2535777606795988, -2.2365806414914347]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E9 28.12.E9] || [[Item:Q8306|<math>\Mathieume{\nu}@{z}{-q} = e^{\iunit\nu\pi/2}\Mathieume{\nu}@{z-\tfrac{1}{2}\pi}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{\nu}@{z}{-q} = e^{\iunit\nu\pi/2}\Mathieume{\nu}@{z-\tfrac{1}{2}\pi}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[\[Nu], - q, z] == Exp[I*\[Nu]*Pi/2]*Sqrt[2]*MathieuC[\[Nu], q, z -Divide[1,2]*Pi]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2866300784936375, -3.291600297925931]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.4943636299546066, 1.4617312701790142]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E10 28.12.E10] || [[Item:Q8307|<math>\conj{\Mathieume{\nu}@{z}{q}} = \Mathieume{\conj{\nu}}@{-\conj{z}}{\conj{q}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\conj{\Mathieume{\nu}@{z}{q}} = \Mathieume{\conj{\nu}}@{-\conj{z}}{\conj{q}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Conjugate[Sqrt[2]*MathieuC[\[Nu], q, z]] == Sqrt[2]*MathieuC[Conjugate[\[Nu]], Conjugate[q], - Conjugate[z]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.449796041425081, -1.3521841059420128]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.040892871573185774, -2.224553529597971]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12#Ex1 28.12#Ex1] || [[Item:Q8308|<math>\Mathieume{n}@{z}{q} = \sqrt{2}\Mathieuce{n}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{n}@{z}{q} = \sqrt{2}\Mathieuce{n}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[n, q, z] == Sqrt[2]*MathieuC[n, q, z]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/28.12#Ex2 28.12#Ex2] || [[Item:Q8309|<math>\Mathieume{-n}@{z}{q} = -\sqrt{2}\iunit\Mathieuse{n}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieume{-n}@{z}{q} = -\sqrt{2}\iunit\Mathieuse{n}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[2]*MathieuC[- n, q, z] == -Sqrt[2]*I*MathieuS[n, q, z]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.6058193733626913, 1.2555909202055446]
-Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.2564301512415783, 3.3896606696156866]
-Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E12 28.12.E12] || [[Item:Q8310|<math>\Mathieuce{\nu}@{z}{q} = \tfrac{1}{2}\left(\Mathieume{\nu}@{z}{q}+\Mathieume{\nu}@{-z}{q}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{\nu}@{z}{q} = \tfrac{1}{2}\left(\Mathieume{\nu}@{z}{q}+\Mathieume{\nu}@{-z}{q}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[\[Nu], q, z] == Divide[1,2]*(Sqrt[2]*MathieuC[\[Nu], q, z]+ Sqrt[2]*MathieuC[\[Nu], q, - z])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.533819042119813, -0.14668719931348273]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3603013806161438, -0.6554927908359449]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E13 28.12.E13] || [[Item:Q8311|<math>\Mathieuse{\nu}@{z}{q} = -\tfrac{1}{2}\iunit\left(\Mathieume{\nu}@{z}{q}-\Mathieume{\nu}@{-z}{q}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{\nu}@{z}{q} = -\tfrac{1}{2}\iunit\left(\Mathieume{\nu}@{z}{q}-\Mathieume{\nu}@{-z}{q}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[\[Nu], q, z] == -Divide[1,2]*I*(Sqrt[2]*MathieuC[\[Nu], q, z]- Sqrt[2]*MathieuC[\[Nu], q, - z])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5117296530175564, 1.1125419914222279]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.502309230543963, -0.7610291346347915]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E14 28.12.E14] || [[Item:Q8312|<math>\Mathieuce{\nu}@{z}{q} = \Mathieuce{\nu}@{-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{\nu}@{z}{q} = \Mathieuce{\nu}@{-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(nu, q, z) = MathieuCE(nu, q, - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[\[Nu], q, z] == MathieuC[\[Nu], q, - z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 300]
-|-
-| [https://dlmf.nist.gov/28.12.E14 28.12.E14] || [[Item:Q8312|<math>\Mathieuce{\nu}@{-z}{q} = \Mathieuce{-\nu}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{\nu}@{-z}{q} = \Mathieuce{-\nu}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(nu, q, - z) = MathieuCE(- nu, q, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[\[Nu], q, - z] == MathieuC[- \[Nu], q, z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.1677458433372196, -0.552801794545088]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.1793065541346438, 1.5815013382691518]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E15 28.12.E15] || [[Item:Q8313|<math>\Mathieuse{\nu}@{z}{q} = -\Mathieuse{\nu}@{-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{\nu}@{z}{q} = -\Mathieuse{\nu}@{-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(nu, q, z) = - MathieuSE(nu, q, - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[\[Nu], q, z] == - MathieuS[\[Nu], q, - z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 300]
-|-
-| [https://dlmf.nist.gov/28.12.E15 28.12.E15] || [[Item:Q8313|<math>-\Mathieuse{\nu}@{-z}{q} = -\Mathieuse{-\nu}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\Mathieuse{\nu}@{-z}{q} = -\Mathieuse{-\nu}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- MathieuSE(nu, q, - z) = - MathieuSE(- nu, q, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- MathieuS[\[Nu], q, - z] == - MathieuS[- \[Nu], q, z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.10223720739540931, 2.122915753327721]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1209568079160426, 0.4323584529351461]
-Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [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.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.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
-|- 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 || - || -
-|- style="background: #dfe6e9;"
-| [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 || - || -
-|- 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 || - || -
-|- 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 || - || -
-|- 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 || - || -
-|- 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/28.19.E4 28.19.E4] || [[Item:Q8332|<math>e^{\iunit\nu z} = \sum_{n=-\infty}^{\infty}c^{\nu+2n}_{-2n}(q)\Mathieume{\nu+2n}@{z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{\iunit\nu z} = \sum_{n=-\infty}^{\infty}c^{\nu+2n}_{-2n}(q)\Mathieume{\nu+2n}@{z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[I*\[Nu]*z] == Sum[(Subscript[c, - 2*n])^(\[Nu]+ 2*n)[q]* Sqrt[2]*MathieuC[\[Nu]+ 2*n, q, z], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.22.E5 28.22.E5] || [[Item:Q8370|<math>g_{\mathit{e},2m}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuce{2m}@{\frac{1}{2}\pi}{h^{2}}}{A_{0}^{2m}(h^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>g_{\mathit{e},2m}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuce{2m}@{\frac{1}{2}\pi}{h^{2}}}{A_{0}^{2m}(h^{2})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>g[e , 2*m](h) = (- 1)^(m)*sqrt((2)/(Pi))*(MathieuCE(2*m, (h)^(2), (1)/(2)*Pi))/((A[0])^(2*m)((h)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[g, e , 2*m][h] == (- 1)^(m)*Sqrt[Divide[2,Pi]]*Divide[MathieuC[2*m, (h)^(2), Divide[1,2]*Pi],(Subscript[A, 0])^(2*m)[(h)^(2)]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[0.42295231653869036, 0.41961671574834936], Power[A, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[Subscript[A, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, E, Times[2, m]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.38839890891671613, -0.3454183210952864], Power[A, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[Subscript[A, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, E, Times[2, m]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.22.E6 28.22.E6] || [[Item:Q8371|<math>g_{\mathit{e},2m+1}(h) = (-1)^{m+1}\sqrt{\frac{2}{\pi}}\dfrac{\Mathieuce{2m+1}'@{\frac{1}{2}\pi}{h^{2}}}{hA_{1}^{2m+1}(h^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>g_{\mathit{e},2m+1}(h) = (-1)^{m+1}\sqrt{\frac{2}{\pi}}\dfrac{\Mathieuce{2m+1}'@{\frac{1}{2}\pi}{h^{2}}}{hA_{1}^{2m+1}(h^{2})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>g[e , 2*m + 1](h) = (- 1)^(m + 1)*sqrt((2)/(Pi))*(subs( temp=(1)/(2)*Pi, diff( MathieuCE(2*m + 1, (h)^(2), temp), temp$(1) ) ))/((hA[1])^(2*m + 1)((h)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[g, e , 2*m + 1][h] == (- 1)^(m + 1)*Sqrt[Divide[2,Pi]]*Divide[D[MathieuC[2*m + 1, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,(Subscript[hA, 1])^(2*m + 1)[(h)^(2)]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.2975776534545682, -0.6256781760348913], Power[A, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[Subscript[A, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, E, Plus[1, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.42963849355864525, 0.8495253193240367], Power[A, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[Subscript[A, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, E, Plus[1, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.22.E7 28.22.E7] || [[Item:Q8372|<math>g_{\mathit{o},2m+1}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+1}@{\frac{1}{2}\pi}{h^{2}}}{hB_{1}^{2m+1}(h^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>g_{\mathit{o},2m+1}(h) = (-1)^{m}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+1}@{\frac{1}{2}\pi}{h^{2}}}{hB_{1}^{2m+1}(h^{2})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>g[o , 2*m + 1](h) = (- 1)^(m)*sqrt((2)/(Pi))*(MathieuSE(2*m + 1, (h)^(2), (1)/(2)*Pi))/((hB[1])^(2*m + 1)((h)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[g, o , 2*m + 1][h] == (- 1)^(m)*Sqrt[Divide[2,Pi]]*Divide[MathieuS[2*m + 1, (h)^(2), Divide[1,2]*Pi],(Subscript[hB, 1])^(2*m + 1)[(h)^(2)]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.32036211571699924, -0.11607109445443671], Power[B, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[o, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, o, Plus[1, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.1322357993555902, 0.30696697344841817], Power[B, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[o, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, o, Plus[1, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.22.E8 28.22.E8] || [[Item:Q8373|<math>g_{\mathit{o},2m+2}(h) = (-1)^{m+1}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+2}'@{\frac{1}{2}\pi}{h^{2}}}{h^{2}B_{2}^{2m+2}(h^{2})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>g_{\mathit{o},2m+2}(h) = (-1)^{m+1}\sqrt{\dfrac{2}{\pi}}\dfrac{\Mathieuse{2m+2}'@{\frac{1}{2}\pi}{h^{2}}}{h^{2}B_{2}^{2m+2}(h^{2})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>g[o , 2*m + 2](h) = (- 1)^(m + 1)*sqrt((2)/(Pi))*(subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*m + 2, (h)^(2), temp), temp$(1) ) ))/((h)^(2)* (B[2])^(2*m + 2)((h)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[g, o , 2*m + 2][h] == (- 1)^(m + 1)*Sqrt[Divide[2,Pi]]*Divide[D[MathieuS[2*m + 2, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,(h)^(2)* (Subscript[B, 2])^(2*m + 2)[(h)^(2)]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[0.09053953879094334, 2.773543957850464], Power[B, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[o, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, o, Plus[2, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.7797636104550828, -1.7837750479423518], Power[B, -1]]]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[o, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[B, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, o, Plus[2, Times[2, m]]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.25.E3 28.25.E3] || [[Item:Q8414|<math>(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{+}_{m+1}+{\left((m+\tfrac{1}{2})^{2}+(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{+}_{m}}+(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{+} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(+)+((m +(1)/(2))^(2)+(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(+)+(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(+) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(+)+((m +Divide[1,2])^(2)+(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(+)+(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(+) == 0</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/28.25.E3 28.25.E3] || [[Item:Q8414|<math>(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(m+1)D^{-}_{m+1}+{\left((m+\tfrac{1}{2})^{2}-(m+\tfrac{1}{4})8\iunit h+2h^{2}-a\right)D^{-}_{m}}-(m-\tfrac{1}{2})\left(8\iunit hm\right)D_{m-1}^{-} = 0</syntaxhighlight> || <math>m \geq 0</math> || <syntaxhighlight lang=mathematica>(m + 1)*(D[m + 1])^(-)+((m +(1)/(2))^(2)-(m +(1)/(4))*8*I*h + 2*(h)^(2)- a)*(D[m])^(-)-(m -(1)/(2))*(8*I*h*m)*(D[m - 1])^(-) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(m + 1)*(Subscript[D, m + 1])^(-)+((m +Divide[1,2])^(2)-(m +Divide[1,4])*8*I*h + 2*(h)^(2)- a)*(Subscript[D, m])^(-)-(m -Divide[1,2])*(8*I*h*m)*(Subscript[D, m - 1])^(-) == 0</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/28.26.E3 28.26.E3] || [[Item:Q8419|<math>\phi = 2h\sinh@@{z}-\left(m+\tfrac{1}{2}\right)\atan@{\sinh@@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi = 2h\sinh@@{z}-\left(m+\tfrac{1}{2}\right)\atan@{\sinh@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi = 2*h*sinh(z)-(m +(1)/(2))*arctan(sinh(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi] == 2*h*Sinh[z]-(m +Divide[1,2])*ArcTan[Sinh[z]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.309060595-.9846819085*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.148731429-.6275515075*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3090605953108105, -0.9846819068983852]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.1487314296378672, -0.6275515058300114]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E1 28.28.E1] || [[Item:Q8422|<math>w = \cosh@@{z}\cos@@{t}\cos@@{\alpha}+\sinh@@{z}\sin@@{t}\sin@@{\alpha}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w = \cosh@@{z}\cos@@{t}\cos@@{\alpha}+\sinh@@{z}\sin@@{t}\sin@@{\alpha}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w = cosh(z)*cos(t)*cos(alpha)+ sinh(z)*sin(t)*sin(alpha)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w == Cosh[z]*Cos[t]*Cos[\[Alpha]]+ Sinh[z]*Sin[t]*Sin[\[Alpha]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.714222282+1.165028049*I
-Test Values: {alpha = 3/2, t = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5264627339+1.356668447*I
-Test Values: {alpha = 3/2, t = -3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7142222818783819, 1.165028048919159]
-Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.2004296775262544, 0.7916410797173274]
-Test Values: {Rule[t, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>0 < \phase@{h(\cosh@@{z}+ 1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>0 < \phase@{h(\cosh@@{z}+ 1)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0 < argument(h*(cosh(z)+ 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 < Arg[h*(Cosh[z]+ 1)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. < -.8396703302
-Test Values: {h = 1/2-1/2*I*3^(1/2), z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < -1.272675688
-Test Values: {h = 1/2-1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>0 < \phase@{h(\cosh@@{z}- 1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>0 < \phase@{h(\cosh@@{z}- 1)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0 < argument(h*(cosh(z)- 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 < Arg[h*(Cosh[z]- 1)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. < -1.643566335
-Test Values: {h = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < -1.643566335
-Test Values: {h = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>\phase@{h(\cosh@@{z}+ 1)} < \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@{h(\cosh@@{z}+ 1)} < \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(h*(cosh(z)+ 1)) < Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[h*(Cosh[z]+ 1)] < Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.141592654
-Test Values: {h = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.141592654
-Test Values: {h = -3/2, z = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, -1.5], Rule[z, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, -1.5], Rule[z, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>\phase@{h(\cosh@@{z}- 1)} < \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phase@{h(\cosh@@{z}- 1)} < \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>argument(h*(cosh(z)- 1)) < Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Arg[h*(Cosh[z]- 1)] < Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.141592654
-Test Values: {h = -3/2, z = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.141592654 < 3.141592654
-Test Values: {h = -3/2, z = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, -1.5], Rule[z, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[h, -1.5], Rule[z, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.28#Ex4 28.28#Ex4] || [[Item:Q8442|<math>R(z,t) = \left(\tfrac{1}{2}(\cosh@{2z}+\cos@{2t})\right)^{\ifrac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>R(z,t) = \left(\tfrac{1}{2}(\cosh@{2z}+\cos@{2t})\right)^{\ifrac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>R(z , t) = ((1)/(2)*(cosh(2*z)+ cos(2*t)))^((1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>R[z , t] == (Divide[1,2]*(Cosh[2*z]+ Cos[2*t]))^(Divide[1,2])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, -1.500000000)-.8604472605-.6693200135*I
-Test Values: {R = 1/2*3^(1/2)+1/2*I, t = -3/2, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(-.5000000000+.8660254040*I, -1.500000000)-.3385916178+.8564557052*I
-Test Values: {R = 1/2*3^(1/2)+1/2*I, t = -3/2, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/28.28#Ex5 28.28#Ex5] || [[Item:Q8443|<math>R(z,0) = \cosh@@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>R(z,0) = \cosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>R(z , 0) = cosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>R[z , 0] == Cosh[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, 0.)-1.227765517-.4690753764*I
-Test Values: {R = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: (.8660254040+.5000000000*I)*(-.5000000000+.8660254040*I, 0.)-.7305430189+.3969495503*I
-Test Values: {R = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/28.28#Ex6 28.28#Ex6] || [[Item:Q8444|<math>e^{2\iunit\phi} = \dfrac{\cosh@{z+\iunit t}}{\cosh@{z-\iunit t}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{2\iunit\phi} = \dfrac{\cosh@{z+\iunit t}}{\cosh@{z-\iunit t}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(2*I*phi) = (cosh(z + I*t))/(cosh(z - I*t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[2*I*\[Phi]] == Divide[Cosh[z + I*t],Cosh[z - I*t]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9781641542+.5339822543*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, t = -3/2, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.021212458+.2569827752*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, t = -3/2, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.978164154574313, 0.5339822543847044]
-Test Values: {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1328205399920523, 0.022001382090719362]
-Test Values: {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.28#Ex7 28.28#Ex7] || [[Item:Q8445|<math>\phi(z,0) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi(z,0) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi(z , 0) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Phi][z , 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.28.E28 28.28.E28] || [[Item:Q8455|<math>\alpha^{(1)}_{\nu,m} = \dfrac{1}{2\pi}\int_{0}^{2\pi}\sin@@{t}\Mathieume{\nu}@{t}{h^{2}}\Mathieume{-\nu-2m-1}@{t}{h^{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\alpha^{(1)}_{\nu,m} = \dfrac{1}{2\pi}\int_{0}^{2\pi}\sin@@{t}\Mathieume{\nu}@{t}{h^{2}}\Mathieume{-\nu-2m-1}@{t}{h^{2}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[\[Alpha], \[Nu], m])^(1) == Divide[1,2*Pi]*Integrate[Sin[t]*Sqrt[2]*MathieuC[\[Nu], (h)^(2), t]*Sqrt[2]*MathieuC[- \[Nu]- 2*m - 1, (h)^(2), t], {t, 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.28.E41 28.28.E41] || [[Item:Q8472|<math>\dfrac{\cosh@@{z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin@@{t}\Mathieuse{n}@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p+1}\iunit h\widehat{\beta}_{n,m}\radMathieuDsc{0}@{n}{m}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\cosh@@{z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin@@{t}\Mathieuse{n}@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p+1}\iunit h\widehat{\beta}_{n,m}\radMathieuDsc{0}@{n}{m}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(cosh(z))/((Pi)^(2))*int((sin(t)*MathieuSE(n, (h)^(2), t)*MathieuCE(m, (h)^(2), t))/((sinh(z))^(2)+ (sin(t))^(2)), t = 0..2*Pi) = (- 1)^(p + 1)* I*h*((1)/(2*Pi)*int(sin(t)*MathieuSE(n, (h)^(2), t)*MathieuCE(m, (h)^(2), t), t = 0..2*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Cosh[z],(Pi)^(2)]*Integrate[Divide[Sin[t]*MathieuS[n, (h)^(2), t]*MathieuC[m, (h)^(2), t],(Sinh[z])^(2)+ (Sin[t])^(2)], {t, 0, 2*Pi}, GenerateConditions->None] == (- 1)^(p + 1)* I*h*(Divide[1,2*Pi]*Integrate[Sin[t]*MathieuS[n, (h)^(2), t]*MathieuC[m, (h)^(2), t], {t, 0, 2*Pi}, GenerateConditions->None])</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/28.28.E42 28.28.E42] || [[Item:Q8473|<math>\dfrac{\sinh@@{z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos@@{t}\Mathieuse{n}'@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p}\iunit h\widehat{\beta}_{n,m}\radMathieuDsc{1}@{n}{m}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\sinh@@{z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos@@{t}\Mathieuse{n}'@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p}\iunit h\widehat{\beta}_{n,m}\radMathieuDsc{1}@{n}{m}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(sinh(z))/((Pi)^(2))*int((cos(t)*subs( temp=t, diff( MathieuSE(n, (h)^(2), temp), temp$(1) ) )*MathieuCE(m, (h)^(2), t))/((sinh(z))^(2)+ (sin(t))^(2)), t = 0..2*Pi) = (- 1)^(p)* I*h*((1)/(2*Pi)*int(sin(t)*MathieuSE(n, (h)^(2), t)*MathieuCE(m, (h)^(2), t), t = 0..2*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Sinh[z],(Pi)^(2)]*Integrate[Divide[Cos[t]*(D[MathieuS[n, (h)^(2), temp], {temp, 1}]/.temp-> t)*MathieuC[m, (h)^(2), t],(Sinh[z])^(2)+ (Sin[t])^(2)], {t, 0, 2*Pi}, GenerateConditions->None] == (- 1)^(p)* I*h*(Divide[1,2*Pi]*Integrate[Sin[t]*MathieuS[n, (h)^(2), t]*MathieuC[m, (h)^(2), t], {t, 0, 2*Pi}, GenerateConditions->None])</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/28.28.E44 28.28.E44] || [[Item:Q8475|<math>\dfrac{1}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin@{2t}\Mathieuse{n}@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p}\iunit\widehat{\gamma}_{n,m}\radMathieuDsc{0}@{n}{m}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{1}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin@{2t}\Mathieuse{n}@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p}\iunit\widehat{\gamma}_{n,m}\radMathieuDsc{0}@{n}{m}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/((Pi)^(2))*int((sin(2*t)*MathieuSE(n, (h)^(2), t)*MathieuCE(m, (h)^(2), t))/((sinh(z))^(2)+ (sin(t))^(2)), t = 0..2*Pi) = (- 1)^(p)* I*((1)/(2*Pi)*int(subs( temp=t, diff( MathieuSE(n, (h)^(2), temp), temp$(1) ) )*MathieuCE(m, (h)^(2), t), t = 0..2*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(Pi)^(2)]*Integrate[Divide[Sin[2*t]*MathieuS[n, (h)^(2), t]*MathieuC[m, (h)^(2), t],(Sinh[z])^(2)+ (Sin[t])^(2)], {t, 0, 2*Pi}, GenerateConditions->None] == (- 1)^(p)* I*(Divide[1,2*Pi]*Integrate[(D[MathieuS[n, (h)^(2), temp], {temp, 1}]/.temp-> t)*MathieuC[m, (h)^(2), t], {t, 0, 2*Pi}, GenerateConditions->None])</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/28.28.E45 28.28.E45] || [[Item:Q8476|<math>\dfrac{\sinh@{2z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\Mathieuse{n}'@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p+1}\iunit\widehat{\gamma}_{n,m}\radMathieuDsc{1}@{n}{m}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\sinh@{2z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\Mathieuse{n}'@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t} = (-1)^{p+1}\iunit\widehat{\gamma}_{n,m}\radMathieuDsc{1}@{n}{m}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(sinh(2*z))/((Pi)^(2))*int((subs( temp=t, diff( MathieuSE(n, (h)^(2), temp), temp$(1) ) )*MathieuCE(m, (h)^(2), t))/((sinh(z))^(2)+ (sin(t))^(2)), t = 0..2*Pi) = (- 1)^(p + 1)* I*((1)/(2*Pi)*int(subs( temp=t, diff( MathieuSE(n, (h)^(2), temp), temp$(1) ) )*MathieuCE(m, (h)^(2), t), t = 0..2*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Sinh[2*z],(Pi)^(2)]*Integrate[Divide[(D[MathieuS[n, (h)^(2), temp], {temp, 1}]/.temp-> t)*MathieuC[m, (h)^(2), t],(Sinh[z])^(2)+ (Sin[t])^(2)], {t, 0, 2*Pi}, GenerateConditions->None] == (- 1)^(p + 1)* I*(Divide[1,2*Pi]*Integrate[(D[MathieuS[n, (h)^(2), temp], {temp, 1}]/.temp-> t)*MathieuC[m, (h)^(2), t], {t, 0, 2*Pi}, GenerateConditions->None])</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.29.E2 28.29.E2] || [[Item:Q8482|<math>Q(z+\pi) = Q(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q(z+\pi) = Q(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q(z + Pi) = Q(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[z + Pi] == Q[z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.29.E3 28.29.E3] || [[Item:Q8483|<math>\int_{0}^{\pi}Q(z)\diff{z} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\pi}Q(z)\diff{z} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(Q(z), z = 0..Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Q[z], {z, 0, Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.273664071+2.467401101*I
-Test Values: {Q = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.467401101+4.273664071*I
-Test Values: {Q = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.2736640683230425, 2.467401100272339]
-Test Values: {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.4674011002723386, 4.2736640683230425]
-Test Values: {Rule[Q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E6 28.29.E6] || [[Item:Q8486|<math>-1 < \realpart@@{\nu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-1 < \realpart@@{\nu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- 1 < Re(nu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- 1 < Re[\[Nu]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1. < -1.500000000
-Test Values: {nu = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1. < -2.
-Test Values: {nu = -2}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[ν, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[ν, -2]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E6 28.29.E6] || [[Item:Q8486|<math>\realpart@@{\nu} \leq 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\realpart@@{\nu} \leq 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Re(nu) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Re[\[Nu]] <= 1</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.500000000 <= 1.
-Test Values: {nu = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2. <= 1.
-Test Values: {nu = 2}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[ν, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: False
-Test Values: {Rule[ν, 2]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E7 28.29.E7] || [[Item:Q8487|<math>w(z+\pi) = e^{\pi\iunit\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi) = e^{\pi\iunit\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi) = exp(Pi*I*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi] == Exp[Pi*I*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.389122976+2.558671223*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.732824151+2.239220255*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.3891229743891893, 2.5586712226918134]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.163689701656905, 2.469736091084983]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.29.E11 28.29.E11] || [[Item:Q8491|<math>w(z+\pi) = (-1)^{\nu}w(z)+cP(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z+\pi) = (-1)^{\nu}w(z)+cP(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z + Pi) = (- 1)^(nu)* w(z)+ cP(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z + Pi] == (- 1)^\[Nu]* w[z]+ cP[z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.29.E13 28.29.E13] || [[Item:Q8493|<math>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi)+ w(z - Pi) = 2*cos(Pi*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi]+ w[z - Pi] == 2*Cos[Pi*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.661616693+6.639028674*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.639028674+1.661616692*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.6616166873386105, 6.63902867151764]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[14.098728614058, -5.830503683799378]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.29.E18 28.29.E18] || [[Item:Q8498|<math>\lambda_{0} < \mu_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda_{0} < \mu_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda[0](<)*mu[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Lambda], 0][<]*Subscript[\[Mu], 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.30.E2 28.30.E2] || [[Item:Q8507|<math>\frac{1}{2\pi}\int_{0}^{2\pi}w_{m}(x)w_{n}(x)\diff{x} = \Kroneckerdelta{m}{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2\pi}\int_{0}^{2\pi}w_{m}(x)w_{n}(x)\diff{x} = \Kroneckerdelta{m}{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2*Pi)*int(w[m](x)* w[n](x), x = 0..2*Pi) = KroneckerDelta[m, n]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2*Pi]*Integrate[Subscript[w, m][x]* Subscript[w, n][x], {x, 0, 2*Pi}, GenerateConditions->None] == KroneckerDelta[m, n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 5.579736275+11.39643752*I
-Test Values: {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 6.579736275+11.39643752*I
-Test Values: {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[5.579736267392906, 11.396437515528111]
-Test Values: {Rule[m, 1], Rule[n, 1], Rule[Subscript[w, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[6.579736267392906, 11.396437515528111]
-Test Values: {Rule[m, 1], Rule[n, 2], Rule[Subscript[w, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex1 28.31#Ex1] || [[Item:Q8511|<math>\xi^{2} = -4k^{2}c^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\xi^{2} = -4k^{2}c^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(xi)^(2) = - 4*(k)^(2)* (c)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Xi]^(2) == - 4*(k)^(2)* (c)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex2 28.31#Ex2] || [[Item:Q8512|<math>A = \eta-\tfrac{1}{8}\xi^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A = \eta-\tfrac{1}{8}\xi^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A = eta -(1)/(8)*(xi)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A == \[Eta]-Divide[1,8]*\[Xi]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex3 28.31#Ex3] || [[Item:Q8513|<math>B = -(p+1)\xi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B = -(p+1)\xi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B = -(p + 1)*xi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B == -(p + 1)*\[Xi]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.31#Ex4 28.31#Ex4] || [[Item:Q8514|<math>W(z) = w(z)\exp@{-\tfrac{1}{4}\xi\cos@{2z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>W(z) = w(z)\exp@{-\tfrac{1}{4}\xi\cos@{2z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>W(z) = w(z)* exp(-(1)/(4)*xi*cos(2*z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>W[z] == w[z]* Exp[-Divide[1,4]*\[Xi]*Cos[2*z]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2817275679-.201842736e-1*I
-Test Values: {W = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5394015055-.3903737220*I
-Test Values: {W = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2817275677812313, -0.02018427332482242]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.06489049435577782, 0.2500000224743827]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.31.E4 28.31.E4] || [[Item:Q8516|<math>w_{\mathit{e},s}(z) = \sum_{\ell=0}^{\infty}A_{2\ell+s}\cos@@{(2\ell+s)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{\mathit{e},s}(z) = \sum_{\ell=0}^{\infty}A_{2\ell+s}\cos@@{(2\ell+s)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[e , s](z) = sum(A[2*ell + s]*cos((2*ell + s)*z), ell = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, e , s][z] == Sum[Subscript[A, 2*\[ScriptL]+ s]*Cos[(2*\[ScriptL]+ s)*z], {\[ScriptL], 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Skip - No test values generated
-|-
-| [https://dlmf.nist.gov/28.31.E5 28.31.E5] || [[Item:Q8517|<math>w_{\mathit{o},s}(z) = \sum_{\ell=0}^{\infty}B_{2\ell+s}\sin@@{(2\ell+s)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{\mathit{o},s}(z) = \sum_{\ell=0}^{\infty}B_{2\ell+s}\sin@@{(2\ell+s)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[o , s](z) = sum(B[2*ell + s]*sin((2*ell + s)*z), ell = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, o , s][z] == Sum[Subscript[B, 2*\[ScriptL]+ s]*Sin[(2*\[ScriptL]+ s)*z], {\[ScriptL], 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Skip - No test values generated
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex5 28.31#Ex5] || [[Item:Q8518|<math>-2\eta A_{0}+(2+p)\xi A_{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>-2\eta A_{0}+(2+p)\xi A_{2} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 2*eta*A[0]+(2 + p)*xi*A[2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 2*\[Eta]*Subscript[A, 0]+(2 + p)*\[Xi]*Subscript[A, 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex6 28.31#Ex6] || [[Item:Q8519|<math>p\xi A_{0}+(4-\eta)A_{2}+\left(\tfrac{1}{2}p+2\right)\xi A_{4} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p\xi A_{0}+(4-\eta)A_{2}+\left(\tfrac{1}{2}p+2\right)\xi A_{4} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p*xi*A[0]+(4 - eta)*A[2]+((1)/(2)*p + 2)*xi*A[4] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p*\[Xi]*Subscript[A, 0]+(4 - \[Eta])*Subscript[A, 2]+(Divide[1,2]*p + 2)*\[Xi]*Subscript[A, 4] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex7 28.31#Ex7] || [[Item:Q8520|<math>(\tfrac{1}{2}p-\ell+1)\xi A_{2\ell-2}+\left(4\ell^{2}-\eta\right)A_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi A_{2\ell+2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\tfrac{1}{2}p-\ell+1)\xi A_{2\ell-2}+\left(4\ell^{2}-\eta\right)A_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi A_{2\ell+2} = 0</syntaxhighlight> || <math>\ell \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*p - ell + 1)*xi*A[2*ell - 2]+(4*(ell)^(2)- eta)*A[2*ell]+((1)/(2)*p + ell + 1)*xi*A[2*ell + 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*p - \[ScriptL]+ 1)*\[Xi]*Subscript[A, 2*\[ScriptL]- 2]+(4*\[ScriptL]^(2)- \[Eta])*Subscript[A, 2*\[ScriptL]]+(Divide[1,2]*p + \[ScriptL]+ 1)*\[Xi]*Subscript[A, 2*\[ScriptL]+ 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex8 28.31#Ex8] || [[Item:Q8521|<math>\left(1-\eta+\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)A_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi A_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\eta+\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)A_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi A_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 - eta +((1)/(2)*p +(1)/(2))*xi)*A[1]+((1)/(2)*p +(3)/(2))*xi*A[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 - \[Eta]+(Divide[1,2]*p +Divide[1,2])*\[Xi])*Subscript[A, 1]+(Divide[1,2]*p +Divide[3,2])*\[Xi]*Subscript[A, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex9 28.31#Ex9] || [[Item:Q8522|<math>(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi A_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)A_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi A_{2\ell+3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi A_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)A_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi A_{2\ell+3} = 0</syntaxhighlight> || <math>\ell \geq 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*p - ell +(1)/(2))*xi*A[2*ell - 1]+((2*ell + 1)^(2)- eta)*A[2*ell + 1]+((1)/(2)*p + ell +(3)/(2))*xi*A[2*ell + 3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*p - \[ScriptL]+Divide[1,2])*\[Xi]*Subscript[A, 2*\[ScriptL]- 1]+((2*\[ScriptL]+ 1)^(2)- \[Eta])*Subscript[A, 2*\[ScriptL]+ 1]+(Divide[1,2]*p + \[ScriptL]+Divide[3,2])*\[Xi]*Subscript[A, 2*\[ScriptL]+ 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex10 28.31#Ex10] || [[Item:Q8523|<math>\left(1-\eta-\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)B_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi B_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\eta-\left(\tfrac{1}{2}p+\tfrac{1}{2}\right)\xi\right)B_{1}+\left(\tfrac{1}{2}p+\tfrac{3}{2}\right)\xi B_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 - eta -((1)/(2)*p +(1)/(2))*xi)*B[1]+((1)/(2)*p +(3)/(2))*xi*B[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 - \[Eta]-(Divide[1,2]*p +Divide[1,2])*\[Xi])*Subscript[B, 1]+(Divide[1,2]*p +Divide[3,2])*\[Xi]*Subscript[B, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex11 28.31#Ex11] || [[Item:Q8524|<math>(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi B_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)B_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi B_{2\ell+3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\tfrac{1}{2}p-\ell+\tfrac{1}{2})\xi B_{2\ell-1}+\left((2\ell+1)^{2}-\eta\right)B_{2\ell+1}+(\tfrac{1}{2}p+\ell+\tfrac{3}{2})\xi B_{2\ell+3} = 0</syntaxhighlight> || <math>\ell \geq 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*p - ell +(1)/(2))*xi*B[2*ell - 1]+((2*ell + 1)^(2)- eta)*B[2*ell + 1]+((1)/(2)*p + ell +(3)/(2))*xi*B[2*ell + 3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*p - \[ScriptL]+Divide[1,2])*\[Xi]*Subscript[B, 2*\[ScriptL]- 1]+((2*\[ScriptL]+ 1)^(2)- \[Eta])*Subscript[B, 2*\[ScriptL]+ 1]+(Divide[1,2]*p + \[ScriptL]+Divide[3,2])*\[Xi]*Subscript[B, 2*\[ScriptL]+ 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex12 28.31#Ex12] || [[Item:Q8525|<math>(4-\eta)B_{2}+\left(\tfrac{1}{2}p+2\right)\xi B_{4} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(4-\eta)B_{2}+\left(\tfrac{1}{2}p+2\right)\xi B_{4} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(4 - eta)*B[2]+((1)/(2)*p + 2)*xi*B[4] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(4 - \[Eta])*Subscript[B, 2]+(Divide[1,2]*p + 2)*\[Xi]*Subscript[B, 4] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex13 28.31#Ex13] || [[Item:Q8526|<math>(\tfrac{1}{2}p-\ell+1)\xi B_{2\ell-2}+(4\ell^{2}-\eta)B_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi B_{2\ell+2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\tfrac{1}{2}p-\ell+1)\xi B_{2\ell-2}+(4\ell^{2}-\eta)B_{2\ell}+(\tfrac{1}{2}p+\ell+1)\xi B_{2\ell+2} = 0</syntaxhighlight> || <math>\ell \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*p - ell + 1)*xi*B[2*ell - 2]+(4*(ell)^(2)- eta)*B[2*ell]+((1)/(2)*p + ell + 1)*xi*B[2*ell + 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*p - \[ScriptL]+ 1)*\[Xi]*Subscript[B, 2*\[ScriptL]- 2]+(4*\[ScriptL]^(2)- \[Eta])*Subscript[B, 2*\[ScriptL]]+(Divide[1,2]*p + \[ScriptL]+ 1)*\[Xi]*Subscript[B, 2*\[ScriptL]+ 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.31.E12 28.31.E12] || [[Item:Q8529|<math>\dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\diff{x} = \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\diff{x} = \dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(((C[p])^(m)(x , xi))^(2), x = 0..2*Pi) = (1)/(Pi)*int(((S[p])^(m)(x , xi))^(2), x = 0..2*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[((Subscript[C, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Divide[1,Pi]*Integrate[((Subscript[S, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.31.E12 28.31.E12] || [[Item:Q8529|<math>\dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\diff{x} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(Pi)*int(((S[p])^(m)(x , xi))^(2), x = 0..2*Pi) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Pi]*Integrate[((Subscript[S, p])^(m)[x , \[Xi]])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == 1</syntaxhighlight> || Failure || Failure || Error || Error
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex22 28.31#Ex22] || [[Item:Q8541|<math>\mathit{hc}_{2n}^{2m}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n}^{2m}(\tfrac{1}{2}\pi-z,\xi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathit{hc}_{2n}^{2m}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n}^{2m}(\tfrac{1}{2}\pi-z,\xi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(hc[2*n])^(2*m)(z , - xi) = (- 1)^(m)* (hc[2*n])^(2*m)((1)/(2)*Pi - z , xi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[hc, 2*n])^(2*m)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hc, 2*n])^(2*m)[Divide[1,2]*Pi - z , \[Xi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex23 28.31#Ex23] || [[Item:Q8542|<math>\mathit{hc}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathit{hc}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(hc[2*n + 1])^(2*m + 1)(z , - xi) = (- 1)^(m)* (hs[2*n + 1])^(2*m + 1)((1)/(2)*Pi - z , xi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[hc, 2*n + 1])^(2*m + 1)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hs, 2*n + 1])^(2*m + 1)[Divide[1,2]*Pi - z , \[Xi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex24 28.31#Ex24] || [[Item:Q8543|<math>\mathit{hs}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathit{hs}_{2n+1}^{2m+1}(z,-\xi) = (-1)^{m}\mathit{hc}_{2n+1}^{2m+1}(\tfrac{1}{2}\pi-z,\xi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(hs[2*n + 1])^(2*m + 1)(z , - xi) = (- 1)^(m)* (hc[2*n + 1])^(2*m + 1)((1)/(2)*Pi - z , xi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[hs, 2*n + 1])^(2*m + 1)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hc, 2*n + 1])^(2*m + 1)[Divide[1,2]*Pi - z , \[Xi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.31#Ex25 28.31#Ex25] || [[Item:Q8544|<math>\mathit{hs}_{2n+2}^{2m+2}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+2}^{2m+2}(\tfrac{1}{2}\pi-z,\xi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathit{hs}_{2n+2}^{2m+2}(z,-\xi) = (-1)^{m}\mathit{hs}_{2n+2}^{2m+2}(\tfrac{1}{2}\pi-z,\xi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(hs[2*n + 2])^(2*m + 2)(z , - xi) = (- 1)^(m)* (hs[2*n + 2])^(2*m + 2)((1)/(2)*Pi - z , xi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[hs, 2*n + 2])^(2*m + 2)[z , - \[Xi]] == (- 1)^(m)* (Subscript[hs, 2*n + 2])^(2*m + 2)[Divide[1,2]*Pi - z , \[Xi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.31.E21 28.31.E21] || [[Item:Q8545|<math>\int_{0}^{2\pi}\mathit{hc}_{p}^{m_{1}}(x,\xi)\mathit{hc}_{p}^{m_{2}}(x,\xi)\diff{x} = \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\mathit{hc}_{p}^{m_{1}}(x,\xi)\mathit{hc}_{p}^{m_{2}}(x,\xi)\diff{x} = \int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((hc[p])^(m[1])(x , xi)* (hc[p])^(m[2])(x , xi), x = 0..2*Pi) = int((hs[p])^(m[1])(x , xi)* (hs[p])^(m[2])(x , xi), x = 0..2*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(Subscript[hc, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hc, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None] == Integrate[(Subscript[hs, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hs, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Manual Skip! || Error
-|-
-| [https://dlmf.nist.gov/28.31.E21 28.31.E21] || [[Item:Q8545|<math>\int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\mathit{hs}_{p}^{m_{1}}(x,\xi)\mathit{hs}_{p}^{m_{2}}(x,\xi)\diff{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((hs[p])^(m[1])(x , xi)* (hs[p])^(m[2])(x , xi), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(Subscript[hs, p])^(Subscript[m, 1])[x , \[Xi]]* (Subscript[hs, p])^(Subscript[m, 2])[x , \[Xi]], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Manual Skip! || Error
-|-
-| [https://dlmf.nist.gov/28.31.E22 28.31.E22] || [[Item:Q8546|<math>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hc}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(int((hc[p[1]])^(m[1])(u , xi)* (hc[p[1]])^(m[1])(v , xi)* (hc[p[2]])^(m[2])(u , xi)* (hc[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Integrate[(Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hc, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hc, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.31.E23 28.31.E23] || [[Item:Q8547|<math>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(int((hs[p[1]])^(m[1])(u , xi)* (hs[p[1]])^(m[1])(v , xi)* (hs[p[2]])^(m[2])(u , xi)* (hs[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Integrate[(Subscript[hs, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hs, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.31.E24 28.31.E24] || [[Item:Q8548|<math>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos@{2u}-\cos@{2v}\right)\diff{v}\diff{u} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(int((hc[p[1]])^(m[1])(u , xi)* (hc[p[1]])^(m[1])(v , xi)* (hs[p[2]])^(m[2])(u , xi)* (hs[p[2]])^(m[2])(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Integrate[(Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[u , \[Xi]]* (Subscript[hc, Subscript[p, 1]])^(Subscript[m, 1])[v , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[u , \[Xi]]* (Subscript[hs, Subscript[p, 2]])^(Subscript[m, 2])[v , \[Xi]]*(Cos[2*u]- Cos[2*v]), {v, 0, 2*Pi}, GenerateConditions->None], {u, Subscript[u, 0], Subscript[u, Infinity]}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.32#Ex1 28.32#Ex1] || [[Item:Q8549|<math>x = c\cosh@@{\xi}\cos@@{\eta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = c\cosh@@{\xi}\cos@@{\eta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = c*cosh(xi)*cos(eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == c*Cosh[\[Xi]]*Cos[\[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.124702180-.2170218424*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.064186236-.8699661686*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.124702180526338, -0.2170218422419914]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.0641862358993213, -0.869966168513175]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32#Ex2 28.32#Ex2] || [[Item:Q8550|<math>y = c\sinh@@{\xi}\sin@@{\eta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = c\sinh@@{\xi}\sin@@{\eta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = c*sinh(xi)*sin(eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == c*Sinh[\[Xi]]*Sin[\[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7333267200+1.299026649*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.266673280+1.299026649*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.7333267206780307, 1.2990266484068542]
-Test Values: {Rule[c, -1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.3699661685131748, 0.9358137641006792]
-Test Values: {Rule[c, -1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32.E2 28.32.E2] || [[Item:Q8551|<math>\pderiv[2]{V}{x}+\pderiv[2]{V}{y}+k^{2}V = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{V}{x}+\pderiv[2]{V}{y}+k^{2}V = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(V, [x$(2)])+ diff(V, [y$(2)])+ (k)^(2)* V = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[V, {x, 2}]+ D[V, {y, 2}]+ (k)^(2)* V == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
-Test Values: {V = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.464101616+2.*I
-Test Values: {V = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
-Test Values: {Rule[k, 1], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.464101615137755, 1.9999999999999998]
-Test Values: {Rule[k, 2], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32.E3 28.32.E3] || [[Item:Q8552|<math>\pderiv[2]{V}{\xi}+\pderiv[2]{V}{\eta}+\frac{1}{2}c^{2}k^{2}(\cosh@{2\xi}-\cos@{2\eta})V = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{V}{\xi}+\pderiv[2]{V}{\eta}+\frac{1}{2}c^{2}k^{2}(\cosh@{2\xi}-\cos@{2\eta})V = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(V, [xi$(2)])+ diff(V, [eta$(2)])+(1)/(2)*(c)^(2)* (k)^(2)*(cosh(2*xi)- cos(2*eta))*V = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[V, {\[Xi], 2}]+ D[V, {\[Eta], 2}]+Divide[1,2]*(c)^(2)* (k)^(2)*(Cosh[2*\[Xi]]- Cos[2*\[Eta]])*V == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1726552223+4.399682965*I
-Test Values: {V = 1/2*3^(1/2)+1/2*I, c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6906208892+17.59873186*I
-Test Values: {V = 1/2*3^(1/2)+1/2*I, c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.172655223437435, 4.399682962494039]
-Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.69062089374974, 17.598731849976154]
-Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32.E4 28.32.E4] || [[Item:Q8553|<math>\pderiv[2]{K}{z}-\pderiv[2]{K}{\zeta} = 2q\left(\cos@{2z}-\cos@{2\zeta}\right)K</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{K}{z}-\pderiv[2]{K}{\zeta} = 2q\left(\cos@{2z}-\cos@{2\zeta}\right)K</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(K, [z$(2)])- diff(K, [zeta$(2)]) = 2*q*(cos(2*z)- cos(2*zeta))*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[K, {z, 2}]- D[K, {\[Zeta], 2}] == 2*q*(Cos[2*z]- Cos[2*\[Zeta]])*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.176649406+6.620283744*I
-Test Values: {K = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4.176649406+6.620283744*I
-Test Values: {K = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-4.176649405937627, 6.620283737597687]
-Test Values: {Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-4.17664940593763, 6.620283737597683]
-Test Values: {Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32#Ex3 28.32#Ex3] || [[Item:Q8556|<math>x_{1} = \tfrac{1}{2}c\left(\cosh@{2\alpha}+\cos@{2\beta}-\cosh@{2\gamma}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{1} = \tfrac{1}{2}c\left(\cosh@{2\alpha}+\cos@{2\beta}-\cosh@{2\gamma}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[1] = (1)/(2)*c*(cosh(2*alpha)+ cos(2*beta)- cosh(2*gamma))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, 1] == Divide[1,2]*c*(Cosh[2*\[Alpha]]+ Cos[2*\[Beta]]- Cosh[2*\[Gamma]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 6.366481639+.5000000000*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 5.000456235+.8660254040*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[6.493212844498693, -1.2277437153775796]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[5.127187440714255, -0.8617183115931409]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32#Ex4 28.32#Ex4] || [[Item:Q8557|<math>x_{2} = 2c\cosh@@{\alpha}\cos@@{\beta}\sinh@@{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{2} = 2c\cosh@@{\alpha}\cos@@{\beta}\sinh@@{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[2] = 2*c*cosh(alpha)*cos(beta)*sinh(gamma)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, 2] == 2*c*Cosh[\[Alpha]]*Cos[\[Beta]]*Sinh[\[Gamma]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.170446049+.5000000000*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1955793552+.8660254040*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2946642543328961, 0.8348348760715232]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.07136114945154226, 1.200860279855962]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.32#Ex5 28.32#Ex5] || [[Item:Q8558|<math>x_{3} = 2c\sinh@@{\alpha}\sin@@{\beta}\cosh@@{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{3} = 2c\sinh@@{\alpha}\sin@@{\beta}\cosh@@{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x[3] = 2*c*sinh(alpha)*sin(beta)*cosh(gamma)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, 3] == 2*c*Sinh[\[Alpha]]*Sin[\[Beta]]*Cosh[\[Gamma]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 8.329140826+.5000000000*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 6.963115422+.8660254040*I
-Test Values: {alpha = 3/2, beta = 3/2, c = -3/2, gamma = 1/2*3^(1/2)+1/2*I, x[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[8.689146837902154, 3.488871718498607]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[7.323121434117715, 3.8548971222830457]
-Test Values: {Rule[c, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/28.33.E1 28.33.E1] || [[Item:Q8560|<math>\pderiv[2]{W}{x}+\pderiv[2]{W}{y}-\frac{\rho}{\tau}\pderiv[2]{W}{t} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[2]{W}{x}+\pderiv[2]{W}{y}-\frac{\rho}{\tau}\pderiv[2]{W}{t} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(W, [x$(2)])+ diff(W, [y$(2)])-(rho)/(tau)*diff(W, [t$(2)]) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[W, {x, 2}]+ D[W, {y, 2}]-Divide[\[Rho],\[Tau]]*D[W, {t, 2}] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
-|}
 </div>

Results of Mathieu Functions and Hill’s Equation: Difference between revisions

Latest revision as of 17:49, 25 May 2021

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