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

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Latest revision as of 17:49, 25 May 2021

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 ${\displaystyle{\displaystyle\mathrm{fe}_{n}}}$ , ${\displaystyle{\displaystyle\mathrm{ge}_{n}}}$
28.6 Expansions for Small ${\displaystyle{\displaystyle q}}$
28.7 Analytic Continuation of Eigenvalues
28.8 Asymptotic Expansions for Large ${\displaystyle{\displaystyle q}}$
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 ${\displaystyle{\displaystyle q}}$
28.16 Asymptotic Expansions for Large ${\displaystyle{\displaystyle q}}$
28.17 Stability as ${\displaystyle{\displaystyle x\to\pm\infty}}$
28.18 Integrals and Integral Equations
28.19 Expansions in Series of ${\displaystyle{\displaystyle\mathrm{me}_{\nu+2n}}}$ 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 ${\displaystyle{\displaystyle\Re z}}$
28.26 Asymptotic Approximations for Large ${\displaystyle{\displaystyle q}}$
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;">
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+; Notation : [[28.1|28.1 Special Notation]]<br>
-! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
+; 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>
-|-
+; 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>
-| [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>]] || <code>S*exp(1)[n]*(s , z) = (MathieuCE(n, q, z))/(MathieuCE(n, q, 0))</code> || <code>S*Subscript[E, n]*(s , z) == Divide[MathieuC[n, q, z],MathieuC[n, q, 0]]</code> || Failure || Failure || Error || Error
+; 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
-|-
+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>
-| [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>]] || <code>S*o[n]*(s , z) = (MathieuSE(n, q, z))/(diff( MathieuSE(n, q, 0), 0$(1) ))</code> || <code>S*Subscript[o, n]*(s , z) == Divide[MathieuS[n, q, z],D[MathieuS[n, q, 0], {0, 1}]]</code> || Error || Failure || - || Error
+; Hill’s Equation : [[28.29|28.29 Definitions and Basic Properties]]<br>[[28.30|28.30 Expansions in Series of Eigenfunctions]]<br>[[28.31|28.31 Equations of Whittaker–Hill and Ince]]<br>
-|-
+; Applications : [[28.32|28.32 Mathematical Applications]]<br>[[28.33|28.33 Physical Applications]]<br>
-| [https://dlmf.nist.gov/28.1#Ex17 28.1#Ex17] || [[Item:Q8140|<math>\mathrm{Se}_{n}(c,z) = \dfrac{\Mathieuce{n}@{z}{q}}{\Mathieuce{n}@{0}{q}}</math>]] || <code>S*exp(1)[n]*(c , z) = (MathieuCE(n, q, z))/(MathieuCE(n, q, 0))</code> || <code>S*Subscript[E, n]*(c , z) == Divide[MathieuC[n, q, z],MathieuC[n, q, 0]]</code> || Failure || Failure || Error || Error
+; Computation : [[28.34|28.34 Methods of Computation]]<br>[[28.35|28.35 Tables]]<br>[[28.36|28.36 Software]]<br>
-|-
+</div>
-| [https://dlmf.nist.gov/28.1#Ex18 28.1#Ex18] || [[Item:Q8141|<math>\mathrm{So}_{n}(c,z) = \dfrac{\Mathieuse{n}@{z}{q}}{\Mathieuse{n}'@{0}{q}}</math>]] || <code>S*o[n]*(c , z) = (MathieuSE(n, q, z))/(diff( MathieuSE(n, q, 0), 0$(1) ))</code> || <code>S*Subscript[o, n]*(c , z) == Divide[MathieuS[n, q, z],D[MathieuS[n, q, 0], {0, 1}]]</code> || 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>]] || <code>w*(z + Pi) = exp(Pi*I*nu)*w*(z)</code> || <code>w*(z + Pi) == Exp[Pi*I*\[Nu]]*w*(z)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[3.389122976+2.558671223*I <- {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}</code><br><code>1.732824151+2.239220255*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[3.3891229743891893, 2.5586712226918134] <- {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]]]}</code><br><code>Complex[3.163689701656905, 2.469736091084983] <- {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]]]}</code><br></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>]] || <code>w*(z + Pi)+ w*(z - Pi) = 2*cos(Pi*nu)*w*(z)</code> || <code>w*(z + Pi)+ w*(z - Pi) == 2*Cos[Pi*\[Nu]]*w*(z)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.661616693+6.639028674*I <- {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}</code><br><code>-6.639028674+1.661616692*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Complex[1.6616166873386105, 6.63902867151764] <- {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]]]}</code><br><code>Complex[14.098728614058, -5.830503683799378] <- {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]]]}</code><br></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>]] || <code>w*(z) = sum(c[2*n]*exp(I*(nu + 2*n)* z), n = - infinity..infinity)</code> || <code>w*(z) == Sum[Subscript[c, 2*n]*Exp[I*(\[Nu]+ 2*n)* z], {n, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [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>]] || <code>q*c[2*n + 2]-(a -(nu + 2*n)^(2))* c[2*n]+ q*c[2*n - 2] = 0 ,</code> || <code>q*Subscript[c, 2*n + 2]-(a -(\[Nu]+ 2*n)^(2))* Subscript[c, 2*n]+ q*Subscript[c, 2*n - 2] == 0 ,</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.2.E20 28.2.E20] || [[Item:Q8163|<math>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</math>]] || <code>limit((abs(c[2*n]))^(1/abs(n)), n = + infinity) = 0</code> || <code>Limit[(Abs[Subscript[c, 2*n]])^(1/Abs[n]), n -> + Infinity, GenerateConditions->None] == 0</code> || 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>]] || <code>MathieuA(n, 0) = (n)^(2)</code> || <code>MathieuCharacteristicA[n, 0] == (n)^(2)</code> || Successful || Successful || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/28.2.E24 28.2.E24] || [[Item:Q8167|<math>\Mathieueigvalb{n}@{0} = n^{2}</math>]] || <code>MathieuB(n, 0) = (n)^(2)</code> || <code>MathieuCharacteristicB[n, 0] == (n)^(2)</code> || 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>]] || <code>MathieuA(2*n, - q) = MathieuA(2*n, q)</code> || <code>MathieuCharacteristicA[2*n, - q] == MathieuCharacteristicA[2*n, q]</code> || 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>]] || <code>MathieuA(2*n + 1, - q) = MathieuB(2*n + 1, q)</code> || <code>MathieuCharacteristicA[2*n + 1, - q] == MathieuCharacteristicB[2*n + 1, q]</code> || 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>]] || <code>MathieuB(2*n + 2, - q) = MathieuB(2*n + 2, q)</code> || <code>MathieuCharacteristicB[2*n + 2, - q] == MathieuCharacteristicB[2*n + 2, q]</code> || 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>]] || <code>MathieuCE(0, 0, z) = 1/(sqrt(2))</code> || <code>MathieuC[0, 0, z] == 1/(Sqrt[2])</code> || 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>]] || <code>MathieuCE(n, 0, z) = cos(n*z)</code> || <code>MathieuC[n, 0, z] == Cos[n*z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><code>{Complex[0.6753267742469401, 0.4379310296367226] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.1123802552186532, 0.12519411502047795] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.2#Ex6 28.2#Ex6] || [[Item:Q8174|<math>\Mathieuse{n}@{z}{0} = \sin@{nz}</math>]] || <code>MathieuSE(n, 0, z) = sin(n*z)</code> || <code>MathieuS[n, 0, z] == Sin[n*z]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><code>{Complex[0.17898073764673827, 1.8916506821927568] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[4.947243351054952, 0.9068272427732345] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>int((MathieuCE(n, q, x))^(2), x = 0..2*Pi) = Pi</code> || <code>Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[6.9214963829238805, 34.195194735367046] <- {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-3.5092269783308243, -0.4627812517943034] <- {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>int((MathieuSE(n, q, x))^(2), x = 0..2*Pi) = Pi</code> || <code>Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 30]<div class="mw-collapsible-content"><code>12/30]: [[-.15495486e-1+.3109277201e-1*I <- {q = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>-1.592260336+2.720760990*I <- {q = 1/2*3^(1/2)+1/2*I, n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[-11.13627493115099, -34.66471446201499] <- {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-4.303849824281496, -4.82944497847242] <- {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>int(MathieuCE(m, q, x)*MathieuCE(n, q, x), x = 0..2*Pi) = 0</code> || <code>Integrate[MathieuC[m, q, x]*MathieuC[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</code> || 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>]] || <code>int(MathieuSE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</code> || <code>Integrate[MathieuS[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</code> || 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>]] || <code>int(MathieuCE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</code> || <code>Integrate[MathieuC[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</code> || 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>]] || <code>MathieuCE(2*n, - q, z) = (- 1)^(n)* MathieuCE(2*n, q, (1)/(2)*Pi - z)</code> || <code>MathieuC[2*n, - q, z] == (- 1)^(n)* MathieuC[2*n, q, Divide[1,2]*Pi - z]</code> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-0.40308591506050084, 0.46785287118948815] <- {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]]]}</code><br><code>Complex[-2.60084404002985, 1.182666432116677] <- {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]]]}</code><br></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>]] || <code>MathieuCE(2*n + 1, - q, z) = (- 1)^(n)* MathieuSE(2*n + 1, q, (1)/(2)*Pi - z)</code> || <code>MathieuC[2*n + 1, - q, z] == (- 1)^(n)* MathieuS[2*n + 1, q, Divide[1,2]*Pi - z]</code> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[1.5024747894079764, -2.6392504264802374] <- {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]]]}</code><br><code>Complex[-2.189026591129222, 0.3274807845663039] <- {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]]]}</code><br></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>]] || <code>MathieuSE(2*n + 1, - q, z) = (- 1)^(n)* MathieuCE(2*n + 1, q, (1)/(2)*Pi - z)</code> || <code>MathieuS[2*n + 1, - q, z] == (- 1)^(n)* MathieuC[2*n + 1, q, Divide[1,2]*Pi - z]</code> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[0.280260494012772, -3.1853558239364403] <- {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]]]}</code><br><code>Complex[-3.634104542197209, -1.1703184896606507] <- {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]]]}</code><br></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>]] || <code>MathieuSE(2*n + 2, - q, z) = (- 1)^(n)* MathieuSE(2*n + 2, q, (1)/(2)*Pi - z)</code> || <code>MathieuS[2*n + 2, - q, z] == (- 1)^(n)* MathieuS[2*n + 2, q, Divide[1,2]*Pi - z]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>210/210]: [[-.3430671662+7.821986266*I <- {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>20.99712460-1.294028748*I <- {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[4.02456715747845, -1.021331524922309] <- {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]]]}</code><br><code>Complex[-2.169415024309792, -3.4466753320968735] <- {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]]]}</code><br></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>]] || <code>MathieuCE(2*n, q, z) sum(A(A[2*m])^(2*n)*(q)* cos(2*m*z), m = 0..infinity)</code> || <code>MathieuC[2*n, q, z] Sum[A(Subscript[A, 2*m])^(2*n)*(q)* Cos[2*m*z], {m, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>MathieuCE(2*n + 1, q, z) sum(A(A[2*m + 1])^(2*n + 1)*(q)* cos((2*m + 1)* z), m = 0..infinity)</code> || <code>MathieuC[2*n + 1, q, z] Sum[A(Subscript[A, 2*m + 1])^(2*n + 1)*(q)* Cos[(2*m + 1)* z], {m, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>MathieuSE(2*n + 1, q, z) sum(B(B[2*m + 1])^(2*n + 1)*(q)* sin((2*m + 1)* z), m = 0..infinity)</code> || <code>MathieuS[2*n + 1, q, z] Sum[B(Subscript[B, 2*m + 1])^(2*n + 1)*(q)* Sin[(2*m + 1)* z], {m, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>MathieuSE(2*n + 2, q, z) sum(B(B[2*m + 2])^(2*n + 2)*(q)* sin((2*m + 2)* z), m = 0..infinity)</code> || <code>MathieuS[2*n + 2, q, z] Sum[B(Subscript[B, 2*m + 2])^(2*n + 2)*(q)* Sin[(2*m + 2)* z], {m, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.4#Ex1 28.4#Ex1] || [[Item:Q8190|<math>aA_{0}-qA_{2} = 0</math>]] || <code>a*A[0]- q*A[2] = 0</code> || <code>a*Subscript[A, 0]- q*Subscript[A, 2] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex2 28.4#Ex2] || [[Item:Q8191|<math>(a-4)A_{2}-q(2A_{0}+A_{4}) = 0</math>]] || <code>(a - 4)* A[2]- q*(2*A[0]+ A[4]) = 0</code> || <code>(a - 4)* Subscript[A, 2]- q*(2*Subscript[A, 0]+ Subscript[A, 4]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(a - 4*(m)^(2))* A[2*m]- q*(A[2*m - 2]+ A[2*m + 2]) = 0</code> || <code>(a - 4*(m)^(2))* Subscript[A, 2*m]- q*(Subscript[A, 2*m - 2]+ Subscript[A, 2*m + 2]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex4 28.4#Ex4] || [[Item:Q8193|<math>(a-1-q)A_{1}-qA_{3} = 0</math>]] || <code>(a - 1 - q)* A[1]- q*A[3] = 0</code> || <code>(a - 1 - q)* Subscript[A, 1]- q*Subscript[A, 3] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(a -(2*m + 1)^(2))* A[2*m + 1]- q*(A[2*m - 1]+ A[2*m + 3]) = 0</code> || <code>(a -(2*m + 1)^(2))* Subscript[A, 2*m + 1]- q*(Subscript[A, 2*m - 1]+ Subscript[A, 2*m + 3]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex6 28.4#Ex6] || [[Item:Q8195|<math>(a-1+q)B_{1}-qB_{3} = 0</math>]] || <code>(a - 1 + q)* B[1]- q*B[3] = 0</code> || <code>(a - 1 + q)* Subscript[B, 1]- q*Subscript[B, 3] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(a -(2*m + 1)^(2))* B[2*m + 1]- q*(B[2*m - 1]+ B[2*m + 3]) = 0</code> || <code>(a -(2*m + 1)^(2))* Subscript[B, 2*m + 1]- q*(Subscript[B, 2*m - 1]+ Subscript[B, 2*m + 3]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex8 28.4#Ex8] || [[Item:Q8197|<math>(a-4)B_{2}-qB_{4} = 0</math>]] || <code>(a - 4)* B[2]- q*B[4] = 0</code> || <code>(a - 4)* Subscript[B, 2]- q*Subscript[B, 4] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(a - 4*(m)^(2))* B[2*m]- q*(B[2*m - 2]+ B[2*m + 2]) = 0</code> || <code>(a - 4*(m)^(2))* Subscript[B, 2*m]- q*(Subscript[B, 2*m - 2]+ Subscript[B, 2*m + 2]) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(A(A[0])^(2*n)*(q))^(2)sum((A(A[2*m])^(2*n)*(q))^(2), m = 1..infinity) = 1</code> || <code>(A(Subscript[A, 0])^(2*n)*(q))^(2)Sum[(A(Subscript[A, 2*m])^(2*n)*(q))^(2), {m, 1, Infinity}, GenerateConditions->None] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>sum((A(A[2*m + 1])^(2*n + 1)*(q))^(2), m = 0..infinity) = 1</code> || <code>Sum[(A(Subscript[A, 2*m + 1])^(2*n + 1)*(q))^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>sum((B(B[2*m + 1])^(2*n + 1)*(q))^(2), m = 0..infinity) = 1</code> || <code>Sum[(B(Subscript[B, 2*m + 1])^(2*n + 1)*(q))^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>sum((B(B[2*m + 2])^(2*n + 2)*(q))^(2), m = 0..infinity) = 1</code> || <code>Sum[(B(Subscript[B, 2*m + 2])^(2*n + 2)*(q))^(2), {m, 0, Infinity}, GenerateConditions->None] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(A[0])^(0)*(0) = 1/(sqrt(2)), (A[2*n])^(2*n)*(0)</code> || <code>(Subscript[A, 0])^(0)*(0) == 1/(Sqrt[2]), (Subscript[A, 2*n])^(2*n)*(0)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex11 28.4#Ex11] || [[Item:Q8204|<math>A^{2n}_{2m}(0) = 0</math>]] || <code>(A[2*m])^(2*n)*(0) = 0</code> || <code>(Subscript[A, 2*m])^(2*n)*(0) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex12 28.4#Ex12] || [[Item:Q8205|<math>A^{2n+1}_{2n+1}(0) = 1</math>]] || <code>(A[2*n + 1])^(2*n + 1)*(0) = 1</code> || <code>(Subscript[A, 2*n + 1])^(2*n + 1)*(0) == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex13 28.4#Ex13] || [[Item:Q8206|<math>A^{2n+1}_{2m+1}(0) = 0</math>]] || <code>(A[2*m + 1])^(2*n + 1)*(0) = 0</code> || <code>(Subscript[A, 2*m + 1])^(2*n + 1)*(0) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex14 28.4#Ex14] || [[Item:Q8207|<math>B^{2n+1}_{2n+1}(0) = 1</math>]] || <code>(B[2*n + 1])^(2*n + 1)*(0) = 1</code> || <code>(Subscript[B, 2*n + 1])^(2*n + 1)*(0) == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex15 28.4#Ex15] || [[Item:Q8208|<math>B^{2n+1}_{2m+1}(0) = 0</math>]] || <code>(B[2*m + 1])^(2*n + 1)*(0) = 0</code> || <code>(Subscript[B, 2*m + 1])^(2*n + 1)*(0) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex16 28.4#Ex16] || [[Item:Q8209|<math>B^{2n+2}_{2n+2}(0) = 1</math>]] || <code>(B[2*n + 2])^(2*n + 2)*(0) = 1</code> || <code>(Subscript[B, 2*n + 2])^(2*n + 2)*(0) == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.4#Ex17 28.4#Ex17] || [[Item:Q8210|<math>B^{2n+2}_{2m+2}(0) = 0</math>]] || <code>(B[2*m + 2])^(2*n + 2)*(0) = 0</code> || <code>(Subscript[B, 2*m + 2])^(2*n + 2)*(0) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(A[2*m])^(2*n)*(- q) = (- 1)^(n - m)* (A[2*m])^(2*n)*(q)</code> || <code>(Subscript[A, 2*m])^(2*n)*(- q) == (- 1)^(n - m)* (Subscript[A, 2*m])^(2*n)*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(B[2*m + 2])^(2*n + 2)*(- q) = (- 1)^(n - m)* (B[2*m + 2])^(2*n + 2)*(q)</code> || <code>(Subscript[B, 2*m + 2])^(2*n + 2)*(- q) == (- 1)^(n - m)* (Subscript[B, 2*m + 2])^(2*n + 2)*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(A[2*m + 1])^(2*n + 1)*(- q) = (- 1)^(n - m)* (B[2*m + 1])^(2*n + 1)*(q)</code> || <code>(Subscript[A, 2*m + 1])^(2*n + 1)*(- q) == (- 1)^(n - m)* (Subscript[B, 2*m + 1])^(2*n + 1)*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(B[2*m + 1])^(2*n + 1)*(- q) = (- 1)^(n - m)* (A[2*m + 1])^(2*n + 1)*(q)</code> || <code>(Subscript[B, 2*m + 1])^(2*n + 1)*(- q) == (- 1)^(n - m)* (Subscript[A, 2*m + 1])^(2*n + 1)*(q)</code> || 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>]] || <code>(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)</code> || <code>(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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>240/300]: [[-165.3668092+.1069227006e-6*I <- {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}</code><br><code>-165.3668092+.1069227006e-6*I <- {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}</code><br></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>]] || <code>(S[n]*(q))^(2)* int((g[n]*(x , q))^(2), x = 0..2*Pi) = Pi</code> || <code>(Subscript[S, n]*(q))^(2)* Integrate[(Subscript[g, n]*(x , q))^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-85.82499725+.5347530766e-7*I <- {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}</code><br><code>-85.82499725+.5347530766e-7*I <- {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}</code><br></div></div> || Error
-|-
-| [https://dlmf.nist.gov/28.5#Ex1 28.5#Ex1] || [[Item:Q8227|<math>C_{2m}(-q) = C_{2m}(q)</math>]] || <code>C[2*m]*(- q) = C[2*m]*(q)</code> || <code>Subscript[C, 2*m]*(- q) == Subscript[C, 2*m]*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.5#Ex2 28.5#Ex2] || [[Item:Q8228|<math>C_{2m+1}(-q) = S_{2m+1}(q)</math>]] || <code>C[2*m + 1]*(- q) = S[2*m + 1]*(q)</code> || <code>Subscript[C, 2*m + 1]*(- q) == Subscript[S, 2*m + 1]*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.5#Ex3 28.5#Ex3] || [[Item:Q8229|<math>S_{2m+2}(-q) = S_{2m+2}(q)</math>]] || <code>S[2*m + 2]*(- q) = S[2*m + 2]*(q)</code> || <code>Subscript[S, 2*m + 2]*(- q) == Subscript[S, 2*m + 2]*(q)</code> || 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>]] || <code>(rho(rho[n])^(j))/((n)^(2)) >= k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2)</code> || <code>Divide[\[Rho](Subscript[\[Rho], n])^(j),(n)^(2)] >= k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2)</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{GreaterEqual[Complex[0.5000000000000001, 0.8660254037844386], Indeterminate] <- {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]]]}</code><br><code>GreaterEqual[Complex[0.12500000000000003, 0.21650635094610965], Indeterminate] <- {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]]]}</code><br></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>]] || <code>k*sqrt(1 - (k)^(2))*(EllipticK(k))^(2) = 2.041834</code> || <code>k*Sqrt[1 - (k)^(2)]*(EllipticK[(k)^2])^(2) == 2.041834</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[k, 1]}</code><br><code>Complex[4.25477173820126, -1.5664714954570549] <- {Rule[k, 2]}</code><br></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>]] || <code>sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0</code> || <code>Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</code> || 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>]] || <code>sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q</code> || <code>Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q</code> || 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>]] || <code>sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q</code> || <code>Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q</code> || 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>]] || <code>sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0</code> || <code>Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</code> || 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>]] || <code>(MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) (W(W[m])^(+)*(x)*(P[m]*(x)- Q[m]*(x))+ W(W[m])^(-)*(x)*(P[m]*(x)+ Q[m]*(x)))</code> || <code>Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] (W(Subscript[W, m])^(+)*(x)*(Subscript[P, m]*(x)- Subscript[Q, m]*(x))+ W(Subscript[W, m])^(-)*(x)*(Subscript[P, m]*(x)+ Subscript[Q, m]*(x)))</code> || 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>]] || <code>(MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) (W(W[m])^(+)*(x)*(P[m]*(x)- Q[m]*(x))- W(W[m])^(-)*(x)*(P[m]*(x)+ Q[m]*(x)))</code> || <code>Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] (W(Subscript[W, m])^(+)*(x)*(Subscript[P, m]*(x)- Subscript[Q, m]*(x))- W(Subscript[W, m])^(-)*(x)*(Subscript[P, m]*(x)+ Subscript[Q, m]*(x)))</code> || 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>]] || <code>(2)/(Pi)*int(cos(2*h*cos(z)*cos(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2)) (A(A[0])^(2*n)*((h)^(2)))/(MathieuCE(2*n, (h)^(2), (1)/(2)*Pi))*MathieuCE(2*n, (h)^(2), z)</code> || <code>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[A(Subscript[A, 0])^(2*n)*((h)^(2)),MathieuC[2*n, (h)^(2), Divide[1,2]*Pi]]*MathieuC[2*n, (h)^(2), z]</code> || 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>]] || <code>(2)/(Pi)*int(cosh(2*h*sin(z)*sin(t))*MathieuCE(2*n, (h)^(2), t), t = 0..(Pi)/(2)) (A(A[0])^(2*n)*((h)^(2)))/(MathieuCE(2*n, (h)^(2), 0))*MathieuCE(2*n, (h)^(2), z)</code> || <code>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[A(Subscript[A, 0])^(2*n)*((h)^(2)),MathieuC[2*n, (h)^(2), 0]]*MathieuC[2*n, (h)^(2), z]</code> || 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>]] || <code>(2)/(Pi)*int(sin(2*h*cos(z)*cos(t))*MathieuCE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) = (h*A(A[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)</code> || <code>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[h*A(Subscript[A, 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]</code> || 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>]] || <code>(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(A[1])^(2*n + 1)*((h)^(2)))/(2*MathieuCE(2*n + 1, (h)^(2), 0))*MathieuCE(2*n + 1, (h)^(2), z)</code> || <code>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[A(Subscript[A, 1])^(2*n + 1)*((h)^(2)),2*MathieuC[2*n + 1, (h)^(2), 0]]*MathieuC[2*n + 1, (h)^(2), z]</code> || 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>]] || <code>(2)/(Pi)*int(sinh(2*h*sin(z)*sin(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) (h*B(B[1])^(2*n + 1)*((h)^(2)))/(subs( temp=0, diff( MathieuSE(2*n + 1, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 1, (h)^(2), z)</code> || <code>Divide[2,Pi]*Integrate[Sinh[2*h*Sin[z]*Sin[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] Divide[h*B(Subscript[B, 1])^(2*n + 1)*((h)^(2)),D[MathieuS[2*n + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0]*MathieuS[2*n + 1, (h)^(2), z]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E6 28.10.E6] || [[Item:Q8285|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\cos@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+1}@{t}{h^{2}}\diff{t} = \frac{B_{1}^{2n+1}(h^{2})}{2\Mathieuse{2n+1}@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+1}@{z}{h^{2}}</math>]] || <code>(2)/(Pi)*int(sin(z)*sin(t)*cos(2*h*cos(z)*cos(t))*MathieuSE(2*n + 1, (h)^(2), t), t = 0..(Pi)/(2)) (B(B[1])^(2*n + 1)*((h)^(2)))/(2*MathieuSE(2*n + 1, (h)^(2), (1)/(2)*Pi))*MathieuSE(2*n + 1, (h)^(2), z)</code> || <code>Divide[2,Pi]*Integrate[Sin[z]*Sin[t]*Cos[2*h*Cos[z]*Cos[t]]*MathieuS[2*n + 1, (h)^(2), t], {t, 0, Divide[Pi,2]}, GenerateConditions->None] Divide[B(Subscript[B, 1])^(2*n + 1)*((h)^(2)),2*MathieuS[2*n + 1, (h)^(2), Divide[1,2]*Pi]]*MathieuS[2*n + 1, (h)^(2), z]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.10.E7 28.10.E7] || [[Item:Q8286|<math>\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin@@{z}\sin@@{t}\sin@{2h\cos@@{z}\cos@@{t}}\Mathieuse{2n+2}@{t}{h^{2}}\diff{t} = -\frac{hB_{2}^{2n+2}(h^{2})}{2\Mathieuse{2n+2}'@{\frac{1}{2}\pi}{h^{2}}}\Mathieuse{2n+2}@{z}{h^{2}}</math>]] || <code>(2)/(Pi)*int(sin(z)*sin(t)*sin(2*h*cos(z)*cos(t))*MathieuSE(2*n + 2, (h)^(2), t), t = 0..(Pi)/(2)) = (h*B(B[2])^(2*n + 2)*((h)^(2)))/(2*subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*n + 2, (h)^(2), temp), temp$(1) ) ))*MathieuSE(2*n + 2, (h)^(2), z)</code> || <code>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[h*B(Subscript[B, 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]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [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>]] || <code>(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)) (h*B(B[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)</code> || <code>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[h*B(Subscript[B, 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]</code> || 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>]] || <code>1 = sum(A(A[0])^(2*n)*(q)* MathieuCE(2*n, q, z), n = 0..infinity)</code> || <code>1 == Sum[A(Subscript[A, 0])^(2*n)*(q)* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>cos(2*m*z) sum(A(A[2*m])^(2*n)*(q)* MathieuCE(2*n, q, z), n = 0..infinity)</code> || <code>Cos[2*m*z] Sum[A(Subscript[A, 2*m])^(2*n)*(q)* MathieuC[2*n, q, z], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>cos((2*m + 1)* z) sum(A(A[2*m + 1])^(2*n + 1)*(q)* MathieuCE(2*n + 1, q, z), n = 0..infinity)</code> || <code>Cos[(2*m + 1)* z] Sum[A(Subscript[A, 2*m + 1])^(2*n + 1)*(q)* MathieuC[2*n + 1, q, z], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>sin((2*m + 1)* z) sum(B(B[2*m + 1])^(2*n + 1)*(q)* MathieuSE(2*n + 1, q, z), n = 0..infinity)</code> || <code>Sin[(2*m + 1)* z] Sum[B(Subscript[B, 2*m + 1])^(2*n + 1)*(q)* MathieuS[2*n + 1, q, z], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>sin((2*m + 2)* z) sum(B(B[2*m + 2])^(2*n + 2)*(q)* MathieuSE(2*n + 2, q, z), n = 0..infinity)</code> || <code>Sin[(2*m + 2)* z] Sum[B(Subscript[B, 2*m + 2])^(2*n + 2)*(q)* MathieuS[2*n + 2, q, z], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[\[Nu], 0, z] == Exp[I*\[Nu]*z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[0.9861942690160291, -0.9067989679250835] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.7892990057566478, 0.4620307840711049] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>Integrate[Sqrt[2]*MathieuC[\[Nu], q, x]*Sqrt[2]*MathieuC[\[Nu], q, - x], {x, 0, Pi}, GenerateConditions->None] == Pi</code> || 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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[\[Nu], q, z + Pi] == Exp[Pi*I*\[Nu]]*Sqrt[2]*MathieuC[\[Nu], q, z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-6.370347292395534, -6.192387567232969] <- {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]]]}</code><br><code>Complex[33.312348543319324, -34.35988503520594] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>Integrate[Sqrt[2]*MathieuC[\[Nu]+ 2*m, q, x]*Sqrt[2]*MathieuC[\[Nu]+ 2*n, q, - x], {x, 0, Pi}, GenerateConditions->None] == 0 ,</code> || 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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[- \[Nu], q, z] == Sqrt[2]*MathieuC[\[Nu], q, - z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-3.065655571425399, 0.7817797951498487] <- {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]]]}</code><br><code>Complex[-0.2535777606795988, -2.2365806414914347] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[\[Nu], - q, z] == Exp[I*\[Nu]*Pi/ 2]*Sqrt[2]*MathieuC[\[Nu], q, z -Divide[1,2]*Pi]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.2866300784936375, -3.291600297925931] <- {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]]]}</code><br><code>Complex[-1.4943636299546066, 1.4617312701790142] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>Conjugate[Sqrt[2]*MathieuC[\[Nu], q, z]] == Sqrt[2]*MathieuC[Conjugate[\[Nu]], Conjugate[q], - Conjugate[z]]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.449796041425081, -1.3521841059420128] <- {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]]]}</code><br><code>Complex[-0.040892871573185774, -2.224553529597971] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[n, q, z] == Sqrt[2]*MathieuC[n, q, z]</code> || 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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[- n, q, z] == -Sqrt[2]*I*MathieuS[n, q, z]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[-2.6058193733626913, 1.2555909202055446] <- {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]]]}</code><br><code>Complex[2.2564301512415783, 3.3896606696156866] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>MathieuC[\[Nu], q, z] == Divide[1,2]*(Sqrt[2]*MathieuC[\[Nu], q, z]+ Sqrt[2]*MathieuC[\[Nu], q, - z])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.533819042119813, -0.14668719931348273] <- {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]]]}</code><br><code>Complex[-0.3603013806161438, -0.6554927908359449] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>MathieuS[\[Nu], q, z] == -Divide[1,2]*I*(Sqrt[2]*MathieuC[\[Nu], q, z]- Sqrt[2]*MathieuC[\[Nu], q, - z])</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.5117296530175564, 1.1125419914222279] <- {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]]]}</code><br><code>Complex[1.502309230543963, -0.7610291346347915] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E14 28.12.E14] || [[Item:Q8312|<math>\Mathieuce{\nu}@{z}{q} = \Mathieuce{\nu}@{-z}{q}</math>]] || <code>MathieuCE(nu, q, z) = MathieuCE(nu, q, - z)</code> || <code>MathieuC[\[Nu], q, z] == MathieuC[\[Nu], q, - z]</code> || 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>]] || <code>MathieuCE(nu, q, - z) = MathieuCE(- nu, q, z)</code> || <code>MathieuC[\[Nu], q, - z] == MathieuC[- \[Nu], q, z]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[2.1677458433372196, -0.552801794545088] <- {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]]]}</code><br><code>Complex[0.1793065541346438, 1.5815013382691518] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.12.E15 28.12.E15] || [[Item:Q8313|<math>\Mathieuse{\nu}@{z}{q} = -\Mathieuse{\nu}@{-z}{q}</math>]] || <code>MathieuSE(nu, q, z) = - MathieuSE(nu, q, - z)</code> || <code>MathieuS[\[Nu], q, z] == - MathieuS[\[Nu], q, - z]</code> || 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>]] || <code>- MathieuSE(nu, q, - z) = - MathieuSE(- nu, q, z)</code> || <code>- MathieuS[\[Nu], q, - z] == - MathieuS[- \[Nu], q, z]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.10223720739540931, 2.122915753327721] <- {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]]]}</code><br><code>Complex[1.1209568079160426, 0.4323584529351461] <- {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]]]}</code><br></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>]] || <code>Error</code> || <code>Sqrt[2]*MathieuC[\[Nu], q, z] Sum[c(Subscript[c, 2*m])^\[Nu]*(q)* Exp[I*(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>MathieuCE(nu, q, z) sum(c(c[2*m])^(nu)*(q)* cos((nu + 2*m)* z), m = - infinity..infinity)</code> || <code>MathieuC[\[Nu], q, z] Sum[c(Subscript[c, 2*m])^\[Nu]*(q)* Cos[(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>MathieuSE(nu, q, z) sum(c(c[2*m])^(nu)*(q)* sin((nu + 2*m)* z), m = - infinity..infinity)</code> || <code>MathieuS[\[Nu], q, z] Sum[c(Subscript[c, 2*m])^\[Nu]*(q)* Sin[(\[Nu]+ 2*m)* z], {m, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Error || Skipped - Because timed out
-|-
-| [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>]] || <code>q*c[2*m + 2]-(a -(nu + 2*m)^(2))* c[2*m]+ q*c[2*m - 2] = 0</code> || <code>q*Subscript[c, 2*m + 2]-(a -(\[Nu]+ 2*m)^(2))* Subscript[c, 2*m]+ q*Subscript[c, 2*m - 2] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>sum((c(c[2*m])^(nu)*(q))^(2), m = - infinity..infinity) = 1</code> || <code>Sum[(c(Subscript[c, 2*m])^\[Nu]*(q))^(2), {m, - Infinity, Infinity}, GenerateConditions->None] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.14.E7 28.14.E7] || [[Item:Q8320|<math>c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)</math>]] || <code>(c[- 2*m])^(- nu)*(q) = (c[2*m])^(nu)*(q)</code> || <code>(Subscript[c, - 2*m])^(- \[Nu])*(q) == (Subscript[c, 2*m])^\[Nu]*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.14.E8 28.14.E8] || [[Item:Q8321|<math>c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)</math>]] || <code>(c[2*m])^(nu)*(- q) = (- 1)^(m)* (c[2*m])^(nu)*(q)</code> || <code>(Subscript[c, 2*m])^\[Nu]*(- q) == (- 1)^(m)* (Subscript[c, 2*m])^\[Nu]*(q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.14#Ex1 28.14#Ex1] || [[Item:Q8322|<math>c_{0}^{\nu}(0) = 1</math>]] || <code>(c[0])^(nu)*(0) = 1</code> || <code>(Subscript[c, 0])^\[Nu]*(0) == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.14#Ex2 28.14#Ex2] || [[Item:Q8323|<math>c_{2m}^{\nu}(0) = 0</math>]] || <code>(c[2*m])^(nu)*(0) = 0</code> || <code>(Subscript[c, 2*m])^\[Nu]*(0) == 0</code> || 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>]] || <code>Error</code> || <code>Exp[I*\[Nu]*z] Sum[c(Subscript[c, - 2*n])^(\[Nu]+ 2*n)*(q)* Sqrt[2]*MathieuC[\[Nu]+ 2*n, q, z], {n, - Infinity, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>g[exp(1), 2*m]*(h) = (- 1)^(m)*(MathieuCE(2*m, (h)^(2), (1)/(2)*Pi))/(A(A[0])^(2*m)*((h)^(2)))</code> || <code>Subscript[g, E , 2*m]*(h) == (- 1)^(m)*Divide[MathieuC[2*m, (h)^(2), Divide[1,2]*Pi],A(Subscript[A, 0])^(2*m)*((h)^(2))]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[0.42295231653869036, 0.41961671574834936], Power[A, -1]]] <- {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]]]}</code><br><code>Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.38839890891671613, -0.3454183210952864], Power[A, -1]]] <- {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]]]}</code><br></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>]] || <code>g[exp(1), 2*m + 1]*(h) = (- 1)^(m + 1)*(subs( temp=(1)/(2)*Pi, diff( MathieuCE(2*m + 1, (h)^(2), temp), temp$(1) ) ))/(h*A(A[1])^(2*m + 1)*((h)^(2)))</code> || <code>Subscript[g, E , 2*m + 1]*(h) == (- 1)^(m + 1)*Divide[D[MathieuC[2*m + 1, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,h*A(Subscript[A, 1])^(2*m + 1)*((h)^(2))]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.2975776534545682, -0.6256781760348913], Power[A, -1]]] <- {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]]]}</code><br><code>Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.42963849355864525, 0.8495253193240367], Power[A, -1]]] <- {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]]]}</code><br></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>]] || <code>g[o , 2*m + 1]*(h) = (- 1)^(m)*(MathieuSE(2*m + 1, (h)^(2), (1)/(2)*Pi))/(h*B(B[1])^(2*m + 1)*((h)^(2)))</code> || <code>Subscript[g, o , 2*m + 1]*(h) == (- 1)^(m)*Divide[MathieuS[2*m + 1, (h)^(2), Divide[1,2]*Pi],h*B(Subscript[B, 1])^(2*m + 1)*((h)^(2))]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.32036211571699924, -0.11607109445443671], Power[B, -1]]] <- {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]]]}</code><br><code>Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.1322357993555902, 0.30696697344841817], Power[B, -1]]] <- {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]]]}</code><br></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>]] || <code>g[o , 2*m + 2]*(h) = (- 1)^(m + 1)*(subs( temp=(1)/(2)*Pi, diff( MathieuSE(2*m + 2, (h)^(2), temp), temp$(1) ) ))/((h)^(2)* B(B[2])^(2*m + 2)*((h)^(2)))</code> || <code>Subscript[g, o , 2*m + 2]*(h) == (- 1)^(m + 1)*Divide[D[MathieuS[2*m + 2, (h)^(2), temp], {temp, 1}]/.temp-> Divide[1,2]*Pi,(h)^(2)* B(Subscript[B, 2])^(2*m + 2)*((h)^(2))]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[0.09053953879094334, 2.773543957850464], Power[B, -1]]] <- {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]]]}</code><br><code>Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-0.7797636104550828, -1.7837750479423518], Power[B, -1]]] <- {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]]]}</code><br></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>]] || <code>(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</code> || <code>(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</code> || 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>]] || <code>(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</code> || <code>(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</code> || 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>]] || <code>phi = 2*h*sinh(z)-(m +(1)/(2))* arctan(sinh(z))</code> || <code>\[Phi] == 2*h*Sinh[z]-(m +Divide[1,2])* ArcTan[Sinh[z]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.309060595-.9846819085*I <- {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}</code><br><code>2.148731429-.6275515075*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.3090605953108105, -0.9846819068983852] <- {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]]]}</code><br><code>Complex[2.1487314296378672, -0.6275515058300114] <- {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]]]}</code><br></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>]] || <code>w = cosh(z)*cos(t)*cos(alpha)+ sinh(z)*sin(t)*sin(alpha)</code> || <code>w == Cosh[z]*Cos[t]*Cos[\[Alpha]]+ Sinh[z]*Sin[t]*Sin[\[Alpha]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><code>299/300]: [[1.714222282+1.165028049*I <- {alpha = 3/2, t = -3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>.5264627339+1.356668447*I <- {alpha = 3/2, t = -3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>{Complex[1.7142222818783819, 1.165028048919159] <- {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]}</code><br><code>Complex[1.2004296775262544, 0.7916410797173274] <- {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]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>0 < \phase@{h(\cosh@@{z}+ 1)}</math>]] || <code>0 < argument(h*(cosh(z)+ 1))</code> || <code>0 < Arg[h*(Cosh[z]+ 1)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><code>35/70]: [[0. < -.8396703302 <- {h = 1/2-1/2*I*3^(1/2), z = 1/2*3^(1/2)+1/2*I}</code><br><code>0. < -1.272675688 <- {h = 1/2-1/2*I*3^(1/2), z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><code>{False <- {Rule[h, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>False <- {Rule[h, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>0 < \phase@{h(\cosh@@{z}- 1)}</math>]] || <code>0 < argument(h*(cosh(z)- 1))</code> || <code>0 < Arg[h*(Cosh[z]- 1)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><code>35/70]: [[0. < -1.643566335 <- {h = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>0. < -1.643566335 <- {h = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [35 / 70]<div class="mw-collapsible-content"><code>{False <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br><code>False <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>\phase@{h(\cosh@@{z}+ 1)} < \pi</math>]] || <code>argument(h*(cosh(z)+ 1)) < Pi</code> || <code>Arg[h*(Cosh[z]+ 1)] < Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><code>9/70]: [[3.141592654 < 3.141592654 <- {h = -3/2, z = 3/2}</code><br><code>3.141592654 < 3.141592654 <- {h = -3/2, z = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><code>{False <- {Rule[h, -1.5], Rule[z, 1.5]}</code><br><code>False <- {Rule[h, -1.5], Rule[z, 0.5]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.28.E10 28.28.E10] || [[Item:Q8434|<math>\phase@{h(\cosh@@{z}- 1)} < \pi</math>]] || <code>argument(h*(cosh(z)- 1)) < Pi</code> || <code>Arg[h*(Cosh[z]- 1)] < Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><code>9/70]: [[3.141592654 < 3.141592654 <- {h = -3/2, z = 3/2}</code><br><code>3.141592654 < 3.141592654 <- {h = -3/2, z = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 70]<div class="mw-collapsible-content"><code>{False <- {Rule[h, -1.5], Rule[z, 1.5]}</code><br><code>False <- {Rule[h, -1.5], Rule[z, 0.5]}</code><br></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>]] || <code>R*(z , t) = ((1)/(2)*(cosh(2*z)+ cos(2*t)))^((1)/(2))</code> || <code>R*(z , t) == (Divide[1,2]*(Cosh[2*z]+ Cos[2*t]))^(Divide[1,2])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[(.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, -1.500000000)-.8604472605-.6693200135*I <- {R = 1/2*3^(1/2)+1/2*I, t = -3/2, z = 1/2*3^(1/2)+1/2*I}</code><br><code>(.8660254040+.5000000000*I)*(-.5000000000+.8660254040*I, -1.500000000)-.3385916178+.8564557052*I <- {R = 1/2*3^(1/2)+1/2*I, t = -3/2, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Error
-|-
-| [https://dlmf.nist.gov/28.28#Ex5 28.28#Ex5] || [[Item:Q8443|<math>R(z,0) = \cosh@@{z}</math>]] || <code>R*(z , 0) = cosh(z)</code> || <code>R*(z , 0) == Cosh[z]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>70/70]: [[(.8660254040+.5000000000*I)*(.8660254040+.5000000000*I, 0.)-1.227765517-.4690753764*I <- {R = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>(.8660254040+.5000000000*I)*(-.5000000000+.8660254040*I, 0.)-.7305430189+.3969495503*I <- {R = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></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>]] || <code>exp(2*I*phi) = (cosh(z + I*t))/(cosh(z - I*t))</code> || <code>Exp[2*I*\[Phi]] == Divide[Cosh[z + I*t],Cosh[z - I*t]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.9781641542+.5339822543*I <- {phi = 1/2*3^(1/2)+1/2*I, t = -3/2, z = 1/2*3^(1/2)+1/2*I}</code><br><code>1.021212458+.2569827752*I <- {phi = 1/2*3^(1/2)+1/2*I, t = -3/2, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.978164154574313, 0.5339822543847044] <- {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]]]}</code><br><code>Complex[1.1328205399920523, 0.022001382090719362] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.28#Ex7 28.28#Ex7] || [[Item:Q8445|<math>\phi(z,0) = 0</math>]] || <code>phi*(z , 0) = 0</code> || <code>\[Phi]*(z , 0) == 0</code> || 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>]] || <code>Error</code> || <code>(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]</code> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/28.29.E2 28.29.E2] || [[Item:Q8482|<math>Q(z+\pi) = Q(z)</math>]] || <code>Q*(z + Pi) = Q*(z)</code> || <code>Q*(z + Pi) == Q*(z)</code> || 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>]] || <code>int(Q*(z), z = 0..Pi) = 0</code> || <code>Integrate[Q*(z), {z, 0, Pi}, GenerateConditions->None] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>10/10]: [[4.273664071+2.467401101*I <- {Q = 1/2*3^(1/2)+1/2*I}</code><br><code>-2.467401101+4.273664071*I <- {Q = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><code>{Complex[4.2736640683230425, 2.467401100272339] <- {Rule[Q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.4674011002723386, 4.2736640683230425] <- {Rule[Q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E6 28.29.E6] || [[Item:Q8486|<math>-1 < \realpart@@{\nu}</math>]] || <code>- 1 < Re(nu)</code> || <code>- 1 < Re[\[Nu]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><code>2/10]: [[-1. < -1.500000000 <- {nu = -3/2}</code><br><code>-1. < -2. <- {nu = -2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><code>{False <- {Rule[ν, -1.5]}</code><br><code>False <- {Rule[ν, -2]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E6 28.29.E6] || [[Item:Q8486|<math>\realpart@@{\nu} \leq 1</math>]] || <code>Re(nu) <= 1</code> || <code>Re[\[Nu]] <= 1</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><code>2/10]: [[1.500000000 <= 1. <- {nu = 3/2}</code><br><code>2. <= 1. <- {nu = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 10]<div class="mw-collapsible-content"><code>{False <- {Rule[ν, 1.5]}</code><br><code>False <- {Rule[ν, 2]}</code><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>]] || <code>w*(z + Pi) = exp(Pi*I*nu)*w*(z)</code> || <code>w*(z + Pi) == Exp[Pi*I*\[Nu]]*w*(z)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[3.389122976+2.558671223*I <- {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}</code><br><code>1.732824151+2.239220255*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[3.3891229743891893, 2.5586712226918134] <- {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]]]}</code><br><code>Complex[3.163689701656905, 2.469736091084983] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E11 28.29.E11] || [[Item:Q8491|<math>w(z+\pi) = (-1)^{\nu}w(z)+cP(z)</math>]] || <code>w*(z + Pi) = (- 1)^(nu)* w*(z)+ c*P*(z)</code> || <code>w*(z + Pi) == (- 1)^\[Nu]* w*(z)+ c*P*(z)</code> || 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>]] || <code>w*(z + Pi)+ w*(z - Pi) = 2*cos(Pi*nu)*w*(z)</code> || <code>w*(z + Pi)+ w*(z - Pi) == 2*Cos[Pi*\[Nu]]*w*(z)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.661616693+6.639028674*I <- {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}</code><br><code>-6.639028674+1.661616692*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Complex[1.6616166873386105, 6.63902867151764] <- {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]]]}</code><br><code>Complex[14.098728614058, -5.830503683799378] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.29.E18 28.29.E18] || [[Item:Q8498|<math>\lambda_{0} < \mu_{1}</math>]] || <code>lambda[0] < mu[1]</code> || <code>Subscript[\[Lambda], 0] < Subscript[\[Mu], 1]</code> || 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>]] || <code>(1)/(2*Pi)*int(w[m]*(x)* w[n]*(x), x = 0..2*Pi) = KroneckerDelta[m, n]</code> || <code>Divide[1,2*Pi]*Integrate[Subscript[w, m]*(x)* Subscript[w, n]*(x), {x, 0, 2*Pi}, GenerateConditions->None] == KroneckerDelta[m, n]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[5.579736275+11.39643752*I <- {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</code><br><code>6.579736275+11.39643752*I <- {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[5.579736267392906, 11.396437515528111] <- {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]]]}</code><br><code>Complex[6.579736267392906, 11.396437515528111] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.31#Ex1 28.31#Ex1] || [[Item:Q8511|<math>\xi^{2} = -4k^{2}c^{2}</math>]] || <code>(xi)^(2) = - 4*(k)^(2)* (c)^(2)</code> || <code>\[Xi]^(2) == - 4*(k)^(2)* (c)^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.31#Ex2 28.31#Ex2] || [[Item:Q8512|<math>A = \eta-\tfrac{1}{8}\xi^{2}</math>]] || <code>A = eta -(1)/(8)*(xi)^(2)</code> || <code>A == \[Eta]-Divide[1,8]*\[Xi]^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/28.31#Ex3 28.31#Ex3] || [[Item:Q8513|<math>B = -(p+1)\xi</math>]] || <code>B = -(p + 1)* xi</code> || <code>B == -(p + 1)* \[Xi]</code> || 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>]] || <code>W*(z) = w*(z)* exp(-(1)/(4)*xi*cos(2*z))</code> || <code>W*(z) == w*(z)* Exp[-Divide[1,4]*\[Xi]*Cos[2*z]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.2817275679-.201842736e-1*I <- {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}</code><br><code>-.5394015055-.3903737220*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.2817275677812313, -0.02018427332482242] <- {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]]]}</code><br><code>Complex[0.06489049435577782, 0.2500000224743827] <- {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]]]}</code><br></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>]] || <code>w[exp(1), s]*(z) = sum(A[2*ell + s]*cos((2*ell + s)* z),  = ..infinity)</code> || <code>Subscript[w, E , s]*(z) == Sum[Subscript[A, 2*\[ScriptL]+ s]*Cos[(2*\[ScriptL]+ s)* z], {, , Infinity}, GenerateConditions->None]</code> || 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>]] || <code>w[o , s]*(z) = sum(B[2*ell + s]*sin((2*ell + s)* z), ell = 0..infinity)</code> || <code>Subscript[w, o , s]*(z) == Sum[Subscript[B, 2*\[ScriptL]+ s]*Sin[(2*\[ScriptL]+ s)* z], {\[ScriptL], 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || - || Skip - No test values generated
-|-
-| [https://dlmf.nist.gov/28.31#Ex5 28.31#Ex5] || [[Item:Q8518|<math>-2\eta A_{0}+(2+p)\xi A_{2} = 0</math>]] || <code>- 2*eta*A[0]+(2 + p)* xi*A[2] = 0</code> || <code>- 2*\[Eta]*Subscript[A, 0]+(2 + p)* \[Xi]*Subscript[A, 2] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>p*xi*A[0]+(4 - eta)* A[2]+((1)/(2)*p + 2)* xi*A[4] = 0</code> || <code>p*\[Xi]*Subscript[A, 0]+(4 - \[Eta])* Subscript[A, 2]+(Divide[1,2]*p + 2)* \[Xi]*Subscript[A, 4] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((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</code> || <code>(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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(1 - eta +((1)/(2)*p +(1)/(2))*xi)* A[1]+((1)/(2)*p +(3)/(2))* xi*A[3] = 0</code> || <code>(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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((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</code> || <code>(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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(1 - eta -((1)/(2)*p +(1)/(2))*xi)* B[1]+((1)/(2)*p +(3)/(2))* xi*B[3] = 0</code> || <code>(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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((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</code> || <code>(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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(4 - eta)* B[2]+((1)/(2)*p + 2)* xi*B[4] = 0</code> || <code>(4 - \[Eta])* Subscript[B, 2]+(Divide[1,2]*p + 2)* \[Xi]*Subscript[B, 4] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((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</code> || <code>(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</code> || 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>]] || <code>int((C(C[p])^(m)*(x , xi))^(2), x = 0..2*Pi) = int((S(S[p])^(m)*(x , xi))^(2), x = 0..2*Pi)</code> || <code>Integrate[(C(Subscript[C, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Integrate[(S(Subscript[S, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}, GenerateConditions->None]</code> || 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>]] || <code>int((S(S[p])^(m)*(x , xi))^(2), x = 0..2*Pi) = 1</code> || <code>Integrate[(S(Subscript[S, p])^(m)*(x , \[Xi]))^(2), {x, 0, 2*Pi}, GenerateConditions->None] == 1</code> || Failure || Failure || Error || Error
-|-
-| [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>]] || <code>h*(c[2*n])^(2*m)*(z , - xi) = (- 1)^(m)* h*(c[2*n])^(2*m)*((1)/(2)*Pi - z , xi)</code> || <code>h*(Subscript[c, 2*n])^(2*m)*(z , - \[Xi]) == (- 1)^(m)* h*(Subscript[c, 2*n])^(2*m)*(Divide[1,2]*Pi - z , \[Xi])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>h*(c[2*n + 1])^(2*m + 1)*(z , - xi) = (- 1)^(m)* h*(s[2*n + 1])^(2*m + 1)*((1)/(2)*Pi - z , xi)</code> || <code>h*(Subscript[c, 2*n + 1])^(2*m + 1)*(z , - \[Xi]) == (- 1)^(m)* h*(Subscript[s, 2*n + 1])^(2*m + 1)*(Divide[1,2]*Pi - z , \[Xi])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>h*(s[2*n + 1])^(2*m + 1)*(z , - xi) = (- 1)^(m)* h*(c[2*n + 1])^(2*m + 1)*((1)/(2)*Pi - z , xi)</code> || <code>h*(Subscript[s, 2*n + 1])^(2*m + 1)*(z , - \[Xi]) == (- 1)^(m)* h*(Subscript[c, 2*n + 1])^(2*m + 1)*(Divide[1,2]*Pi - z , \[Xi])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>h*(s[2*n + 2])^(2*m + 2)*(z , - xi) = (- 1)^(m)* h*(s[2*n + 2])^(2*m + 2)*((1)/(2)*Pi - z , xi)</code> || <code>h*(Subscript[s, 2*n + 2])^(2*m + 2)*(z , - \[Xi]) == (- 1)^(m)* h*(Subscript[s, 2*n + 2])^(2*m + 2)*(Divide[1,2]*Pi - z , \[Xi])</code> || 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>]] || <code>int(h*s(s[p])^(m[1])*(x , xi)* h*s(s[p])^(m[2])*(x , xi), x = 0..2*Pi)</code> || <code>Integrate[h*s(Subscript[s, p])^(Subscript[m, 1])*(x , \[Xi])* h*s(Subscript[s, p])^(Subscript[m, 2])*(x , \[Xi]), {x, 0, 2*Pi}, GenerateConditions->None]</code> || 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>]] || <code>int(h*s(s[p])^(m[1])*(x , xi)* h*s(s[p])^(m[2])*(x , xi), x = 0..2*Pi) = 0</code> || <code>Integrate[h*s(Subscript[s, p])^(Subscript[m, 1])*(x , \[Xi])* h*s(Subscript[s, p])^(Subscript[m, 2])*(x , \[Xi]), {x, 0, 2*Pi}, GenerateConditions->None] == 0</code> || 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>]] || <code>int(int(h*c(c[p[1]])^(m[1])*(u , xi)* h*c(c[p[1]])^(m[1])*(v , xi)* h*c(c[p[2]])^(m[2])*(u , xi)* h*c(c[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</code> || <code>Integrate[Integrate[h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*c(Subscript[c, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*c(Subscript[c, 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</code> || 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>]] || <code>int(int(h*s(s[p[1]])^(m[1])*(u , xi)* h*s(s[p[1]])^(m[1])*(v , xi)* h*s(s[p[2]])^(m[2])*(u , xi)* h*s(s[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</code> || <code>Integrate[Integrate[h*s(Subscript[s, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*s(Subscript[s, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*s(Subscript[s, 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</code> || 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>]] || <code>int(int(h*c(c[p[1]])^(m[1])*(u , xi)* h*c(c[p[1]])^(m[1])*(v , xi)* h*s(s[p[2]])^(m[2])*(u , xi)* h*s(s[p[2]])^(m[2])*(v , xi)*(cos(2*u)- cos(2*v)), v = 0..2*Pi), u = u[0]..u[infinity]) = 0</code> || <code>Integrate[Integrate[h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(u , \[Xi])* h*c(Subscript[c, Subscript[p, 1]])^(Subscript[m, 1])*(v , \[Xi])* h*s(Subscript[s, Subscript[p, 2]])^(Subscript[m, 2])*(u , \[Xi])* h*s(Subscript[s, 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</code> || Failure || Failure || Error || Error
-|-
-| [https://dlmf.nist.gov/28.32#Ex1 28.32#Ex1] || [[Item:Q8549|<math>x = c\cosh@@{\xi}\cos@@{\eta}</math>]] || <code>x = c*cosh(xi)*cos(eta)</code> || <code>x == c*Cosh[\[Xi]]*Cos[\[Eta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[3.124702180-.2170218424*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I}</code><br><code>2.064186236-.8699661686*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[3.124702180526338, -0.2170218422419914] <- {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]]]}</code><br><code>Complex[2.0641862358993213, -0.869966168513175] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/28.32#Ex2 28.32#Ex2] || [[Item:Q8550|<math>y = c\sinh@@{\xi}\sin@@{\eta}</math>]] || <code>y = c*sinh(xi)*sin(eta)</code> || <code>y == c*Sinh[\[Xi]]*Sin[\[Eta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.7333267200+1.299026649*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, y = -3/2}</code><br><code>2.266673280+1.299026649*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, y = 3/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.7333267206780307, 1.2990266484068542] <- {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]]]}</code><br><code>Complex[-2.3699661685131748, 0.9358137641006792] <- {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]]]}</code><br></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>]] || <code>diff(V, [x$(2)])+ diff(V, [y$(2)])+ (k)^(2)* V = 0</code> || <code>D[V, {x, 2}]+ D[V, {y, 2}]+ (k)^(2)* V == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254040+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}</code><br><code>3.464101616+2.*I <- {V = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</code><br><code>Complex[3.464101615137755, 1.9999999999999998] <- {Rule[k, 2], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5]}</code><br></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>]] || <code>diff(V, [xi$(2)])+ diff(V, [eta$(2)])+(1)/(2)*(c)^(2)* (k)^(2)*(cosh(2*xi)- cos(2*eta))* V = 0</code> || <code>D[V, {\[Xi], 2}]+ D[V, {\[Eta], 2}]+Divide[1,2]*(c)^(2)* (k)^(2)*(Cosh[2*\[Xi]]- Cos[2*\[Eta]])* V == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><code>276/300]: [[-.1726552223+4.399682965*I <- {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}</code><br><code>-.6906208892+17.59873186*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.172655223437435, 4.399682962494039] <- {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]]]}</code><br><code>Complex[-0.69062089374974, 17.598731849976154] <- {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]]]}</code><br></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>]] || <code>diff(K, [z$(2)])- diff(K, [zeta$(2)]) = 2*q*(cos(2*z)- cos(2*zeta))* K</code> || <code>D[K, {z, 2}]- D[K, {\[Zeta], 2}] == 2*q*(Cos[2*z]- Cos[2*\[Zeta]])* K</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>240/300]: [[-4.176649406+6.620283744*I <- {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)}</code><br><code>-4.176649406+6.620283744*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Complex[-4.176649405937627, 6.620283737597687] <- {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]]]}</code><br><code>Complex[-4.17664940593763, 6.620283737597683] <- {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]]]}</code><br></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>]] || <code>x[1] = (1)/(2)*c*(cosh(2*alpha)+ cos(2*beta)- cosh(2*gamma))</code> || <code>Subscript[x, 1] == Divide[1,2]*c*(Cosh[2*\[Alpha]]+ Cos[2*\[Beta]]- Cosh[2*\[Gamma]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[6.366481639+.5000000000*I <- {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}</code><br><code>5.000456235+.8660254040*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[6.493212844498693, -1.2277437153775796] <- {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]]]}</code><br><code>Complex[5.127187440714255, -0.8617183115931409] <- {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]]]}</code><br></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>]] || <code>x[2] = 2*c*cosh(alpha)*cos(beta)*sinh(gamma)</code> || <code>Subscript[x, 2] == 2*c*Cosh[\[Alpha]]*Cos[\[Beta]]*Sinh[\[Gamma]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.170446049+.5000000000*I <- {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}</code><br><code>-.1955793552+.8660254040*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.2946642543328961, 0.8348348760715232] <- {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]]]}</code><br><code>Complex[-0.07136114945154226, 1.200860279855962] <- {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]]]}</code><br></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>]] || <code>x[3] = 2*c*sinh(alpha)*sin(beta)*cosh(gamma)</code> || <code>Subscript[x, 3] == 2*c*Sinh[\[Alpha]]*Sin[\[Beta]]*Cosh[\[Gamma]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[8.329140826+.5000000000*I <- {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}</code><br><code>6.963115422+.8660254040*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[8.689146837902154, 3.488871718498607] <- {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]]]}</code><br><code>Complex[7.323121434117715, 3.8548971222830457] <- {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]]]}</code><br></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>]] || <code>diff(W, [x$(2)])+ diff(W, [y$(2)])-(rho)/(tau)*diff(W, [t$(2)]) = 0</code> || <code>D[W, {x, 2}]+ D[W, {y, 2}]-Divide[\[Rho],\[Tau]]*D[W, {t, 2}] == 0</code> || Successful || Successful || - || Successful [Tested: 300]
-|-
-|}

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

Latest revision as of 17:49, 25 May 2021

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