28.2: Difference between revisions

Latest revision as of 12:07, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
28.2.E14	${\displaystyle{\displaystyle w(z+\pi)=e^{\pi\mathrm{i}\nu}w(z)}}$ `w(z+\pi) = e^{\pi\iunit\nu}w(z)`		w(z + Pi) = exp(PiInu)*w(z)	w[z + Pi] == Exp[PiI\[Nu]]*w[z]	Failure	Failure	Failed [300 / 300] Result: 3.389122976+2.558671223I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: 1.732824151+2.239220255I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[3.3891229743891893, 2.5586712226918134] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[3.163689701656905, 2.469736091084983] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
28.2.E17	${\displaystyle{\displaystyle w(z+\pi)+w(z-\pi)=2\cos\left(\pi\nu\right)w(z)}}$ `w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)`		w(z + Pi)+ w(z - Pi) = 2cos(Pinu)*w(z)	w[z + Pi]+ w[z - Pi] == 2Cos[Pi\[Nu]]*w[z]	Failure	Failure	Failed [300 / 300] Result: 1.661616693+6.639028674I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -6.639028674+1.661616692I Test Values: {nu = 1/23^(1/2)+1/2I, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [240 / 300] Result: Complex[1.6616166873386105, 6.63902867151764] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[14.098728614058, -5.830503683799378] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
28.2.E18	${\displaystyle{\displaystyle w(z)=\sum_{n=-\infty}^{\infty}c_{2n}e^{\mathrm{i}% (\nu+2n)z}}}$ `w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}`		w(z) = sum(c[2n]exp(I(nu + 2n)*z), n = - infinity..infinity)	w[z] == Sum[Subscript[c, 2n]Exp[I(\[Nu]+ 2n)*z], {n, - Infinity, Infinity}, GenerateConditions->None]	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.2.E19	${\displaystyle{\displaystyle qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2% n-2}=0,}}$ `qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,`		qc[2n + 2]-(a -(nu + 2n)^(2))c[2n]+ qc[2*n - 2] = 0	qSubscript[c, 2n + 2]-(a -(\[Nu]+ 2n)^(2))Subscript[c, 2n]+ qSubscript[c, 2*n - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
28.2.E20	${\displaystyle{\displaystyle\lim_{n\to+\infty}\|c_{2n}\|^{1/\|n\|}=0}}$ `\lim_{n\to+\infty}\|c_{2n}\|^{1/\|n\|} = 0`		limit((abs(c[2*n]))^(1/abs(n)), n = + infinity) = 0	Limit[(Abs[Subscript[c, 2*n]])^(1/Abs[n]), n -> + Infinity, GenerateConditions->None] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
28.2.E23	${\displaystyle{\displaystyle a_{n}\left(0\right)=n^{2}}}$ `\Mathieueigvala{n}@{0} = n^{2}`		MathieuA(n, 0) = (n)^(2)	MathieuCharacteristicA[n, 0] == (n)^(2)	Successful	Successful	-	Successful [Tested: 1]
28.2.E24	${\displaystyle{\displaystyle b_{n}\left(0\right)=n^{2}}}$ `\Mathieueigvalb{n}@{0} = n^{2}`		MathieuB(n, 0) = (n)^(2)	MathieuCharacteristicB[n, 0] == (n)^(2)	Successful	Successful	-	Successful [Tested: 1]
28.2.E26	${\displaystyle{\displaystyle a_{2n}\left(-q\right)=a_{2n}\left(q\right)}}$ `\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}`		MathieuA(2n, - q) = MathieuA(2n, q)	MathieuCharacteristicA[2n, - q] == MathieuCharacteristicA[2n, q]	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
28.2.E27	${\displaystyle{\displaystyle a_{2n+1}\left(-q\right)=b_{2n+1}\left(q\right)}}$ `\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}`		MathieuA(2n + 1, - q) = MathieuB(2n + 1, q)	MathieuCharacteristicA[2n + 1, - q] == MathieuCharacteristicB[2n + 1, q]	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
28.2.E28	${\displaystyle{\displaystyle b_{2n+2}\left(-q\right)=b_{2n+2}\left(q\right)}}$ `\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}`		MathieuB(2n + 2, - q) = MathieuB(2n + 2, q)	MathieuCharacteristicB[2n + 2, - q] == MathieuCharacteristicB[2n + 2, q]	Failure	Failure	Successful [Tested: 30]	Successful [Tested: 30]
28.2#Ex4	${\displaystyle{\displaystyle\mathrm{ce}_{0}\left(z,0\right)=1/\sqrt{2}}}$ `\Mathieuce{0}@{z}{0} = 1/\sqrt{2}`		MathieuCE(0, 0, z) = 1/(sqrt(2))	MathieuC[0, 0, z] == 1/(Sqrt[2])	Failure	Successful	Skip - No test values generated	Successful [Tested: 7]
28.2#Ex5	${\displaystyle{\displaystyle\mathrm{ce}_{n}\left(z,0\right)=\cos\left(nz\right% )}}$ `\Mathieuce{n}@{z}{0} = \cos@{nz}`		MathieuCE(n, 0, z) = cos(n*z)	MathieuC[n, 0, z] == Cos[n*z]	Successful	Failure	-	Failed [14 / 21] Result: Complex[0.6753267742469401, 0.4379310296367226] Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.1123802552186532, 0.12519411502047795] Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2#Ex6	${\displaystyle{\displaystyle\mathrm{se}_{n}\left(z,0\right)=\sin\left(nz\right% )}}$ `\Mathieuse{n}@{z}{0} = \sin@{nz}`		MathieuSE(n, 0, z) = sin(n*z)	MathieuS[n, 0, z] == Sin[n*z]	Successful	Failure	-	Failed [7 / 7] Result: Complex[0.17898073764673827, 1.8916506821927568] Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[4.947243351054952, 0.9068272427732345] Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
28.2#Ex7	${\displaystyle{\displaystyle\int_{0}^{2\pi}\left(\mathrm{ce}_{n}\left(x,q% \right)\right)^{2}\mathrm{d}x=\pi}}$ `\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi`		int((MathieuCE(n, q, x))^(2), x = 0..2*Pi) = Pi	Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi	Failure	Failure	Skipped - Because timed out	Failed [30 / 30] Result: Complex[6.9214963829238805, 34.195194735367046] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.5092269783308243, -0.4627812517943034] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2#Ex8	${\displaystyle{\displaystyle\int_{0}^{2\pi}\left(\mathrm{se}_{n}\left(x,q% \right)\right)^{2}\mathrm{d}x=\pi}}$ `\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi`		int((MathieuSE(n, q, x))^(2), x = 0..2*Pi) = Pi	Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi	Failure	Failure	Failed [12 / 30] Result: -.15495486e-1+.3109277201e-1I Test Values: {q = 1/23^(1/2)+1/2I, n = 1} Result: -1.592260336+2.720760990I Test Values: {q = 1/23^(1/2)+1/2I, n = 2} ... skip entries to safe data	Failed [30 / 30] Result: Complex[-11.13627493115099, -34.66471446201499] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-4.303849824281496, -4.82944497847242] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2.E31	${\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{ce}_{m}\left(x,q\right)% \mathrm{ce}_{n}\left(x,q\right)\mathrm{d}x=0}}$ `\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0`	${\displaystyle{\displaystyle n\neq m}}$	int(MathieuCE(m, q, x)MathieuCE(n, q, x), x = 0..2Pi) = 0	Integrate[MathieuC[m, q, x]MathieuC[n, q, x], {x, 0, 2Pi}, GenerateConditions->None] == 0	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.2.E32	${\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{se}_{m}\left(x,q\right)% \mathrm{se}_{n}\left(x,q\right)\mathrm{d}x=0}}$ `\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0`	${\displaystyle{\displaystyle n\neq m}}$	int(MathieuSE(m, q, x)MathieuSE(n, q, x), x = 0..2Pi) = 0	Integrate[MathieuS[m, q, x]MathieuS[n, q, x], {x, 0, 2Pi}, GenerateConditions->None] == 0	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.2.E33	${\displaystyle{\displaystyle\int_{0}^{2\pi}\mathrm{ce}_{m}\left(x,q\right)% \mathrm{se}_{n}\left(x,q\right)\mathrm{d}x=0}}$ `\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0`		int(MathieuCE(m, q, x)MathieuSE(n, q, x), x = 0..2Pi) = 0	Integrate[MathieuC[m, q, x]MathieuS[n, q, x], {x, 0, 2Pi}, GenerateConditions->None] == 0	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.2.E34	${\displaystyle{\displaystyle\mathrm{ce}_{2n}\left(z,-q\right)=(-1)^{n}\mathrm{% ce}_{2n}\left(\tfrac{1}{2}\pi-z,q\right)}}$ `\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}`		MathieuCE(2n, - q, z) = (- 1)^(n) MathieuCE(2n, q, (1)/(2)Pi - z)	MathieuC[2n, - q, z] == (- 1)^(n) MathieuC[2n, q, Divide[1,2]Pi - z]	Failure	Failure	Successful [Tested: 210]	Failed [210 / 210] Result: Complex[-0.40308591506050084, 0.46785287118948815] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.60084404002985, 1.182666432116677] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2.E35	${\displaystyle{\displaystyle\mathrm{ce}_{2n+1}\left(z,-q\right)=(-1)^{n}% \mathrm{se}_{2n+1}\left(\tfrac{1}{2}\pi-z,q\right)}}$ `\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}`		MathieuCE(2n + 1, - q, z) = (- 1)^(n) MathieuSE(2n + 1, q, (1)/(2)Pi - z)	MathieuC[2n + 1, - q, z] == (- 1)^(n) MathieuS[2n + 1, q, Divide[1,2]Pi - z]	Failure	Failure	Successful [Tested: 210]	Failed [210 / 210] Result: Complex[1.5024747894079764, -2.6392504264802374] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.189026591129222, 0.3274807845663039] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2.E36	${\displaystyle{\displaystyle\mathrm{se}_{2n+1}\left(z,-q\right)=(-1)^{n}% \mathrm{ce}_{2n+1}\left(\tfrac{1}{2}\pi-z,q\right)}}$ `\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}`		MathieuSE(2n + 1, - q, z) = (- 1)^(n) MathieuCE(2n + 1, q, (1)/(2)Pi - z)	MathieuS[2n + 1, - q, z] == (- 1)^(n) MathieuC[2n + 1, q, Divide[1,2]Pi - z]	Failure	Failure	Successful [Tested: 210]	Failed [210 / 210] Result: Complex[0.280260494012772, -3.1853558239364403] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-3.634104542197209, -1.1703184896606507] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
28.2.E37	${\displaystyle{\displaystyle\mathrm{se}_{2n+2}\left(z,-q\right)=(-1)^{n}% \mathrm{se}_{2n+2}\left(\tfrac{1}{2}\pi-z,q\right)}}$ `\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}`		MathieuSE(2n + 2, - q, z) = (- 1)^(n) MathieuSE(2n + 2, q, (1)/(2)Pi - z)	MathieuS[2n + 2, - q, z] == (- 1)^(n) MathieuS[2n + 2, q, Divide[1,2]Pi - z]	Failure	Failure	Failed [210 / 210] Result: -.3430671662+7.821986266I Test Values: {q = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 1} Result: 20.99712460-1.294028748I Test Values: {q = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I, n = 2} ... skip entries to safe data	Failed [210 / 210] Result: Complex[4.02456715747845, -1.021331524922309] Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.169415024309792, -3.4466753320968735] Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/28.2.E14 28.2.E14] || [[Item:Q8157|<math>w(z+\pi) = e^{\pi\iunit\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi) = e^{\pi\iunit\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi) = exp(Pi*I*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi] == Exp[Pi*I*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.389122976+2.558671223*I
+| [https://dlmf.nist.gov/28.2.E14 28.2.E14] || <math qid="Q8157">w(z+\pi) = e^{\pi\iunit\nu}w(z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi) = e^{\pi\iunit\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi) = exp(Pi*I*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi] == Exp[Pi*I*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.389122976+2.558671223*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.732824151+2.239220255*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.3891229743891893, 2.5586712226918134]
@@ Line 20: / Line 20: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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-| [https://dlmf.nist.gov/28.2.E17 28.2.E17] || [[Item:Q8160|<math>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi)+ w(z - Pi) = 2*cos(Pi*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi]+ w[z - Pi] == 2*Cos[Pi*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.661616693+6.639028674*I
+| [https://dlmf.nist.gov/28.2.E17 28.2.E17] || <math qid="Q8160">w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+\pi)+w(z-\pi) = 2\cos@{\pi\nu}w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + Pi)+ w(z - Pi) = 2*cos(Pi*nu)*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + Pi]+ w[z - Pi] == 2*Cos[Pi*\[Nu]]*w[z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.661616693+6.639028674*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.639028674+1.661616692*I
 Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.6616166873386105, 6.63902867151764]
@@ Line 26: / Line 26: @@
 Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2.E18 28.2.E18] || [[Item:Q8161|<math>w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z) = sum(c[2*n]*exp(I*(nu + 2*n)*z), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z] == Sum[Subscript[c, 2*n]*Exp[I*(\[Nu]+ 2*n)*z], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/28.2.E18 28.2.E18] || <math qid="Q8161">w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z) = \sum_{n=-\infty}^{\infty}c_{2n}e^{\iunit(\nu+2n)z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z) = sum(c[2*n]*exp(I*(nu + 2*n)*z), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z] == Sum[Subscript[c, 2*n]*Exp[I*(\[Nu]+ 2*n)*z], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.2.E19 28.2.E19] || [[Item:Q8162|<math>qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*c[2*n + 2]-(a -(nu + 2*n)^(2))*c[2*n]+ q*c[2*n - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*Subscript[c, 2*n + 2]-(a -(\[Nu]+ 2*n)^(2))*Subscript[c, 2*n]+ q*Subscript[c, 2*n - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/28.2.E19 28.2.E19] || <math qid="Q8162">qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>qc_{2n+2}-\left(a-(\nu+2n)^{2}\right)c_{2n}+qc_{2n-2} = 0,</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*c[2*n + 2]-(a -(nu + 2*n)^(2))*c[2*n]+ q*c[2*n - 2] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q*Subscript[c, 2*n + 2]-(a -(\[Nu]+ 2*n)^(2))*Subscript[c, 2*n]+ q*Subscript[c, 2*n - 2] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/28.2.E20 28.2.E20] || [[Item:Q8163|<math>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((abs(c[2*n]))^(1/abs(n)), n = + infinity) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Abs[Subscript[c, 2*n]])^(1/Abs[n]), n -> + Infinity, GenerateConditions->None] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/28.2.E20 28.2.E20] || <math qid="Q8163">\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{n\to+\infty}|c_{2n}|^{1/|n|} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((abs(c[2*n]))^(1/abs(n)), n = + infinity) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Abs[Subscript[c, 2*n]])^(1/Abs[n]), n -> + Infinity, GenerateConditions->None] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/28.2.E23 28.2.E23] || [[Item:Q8166|<math>\Mathieueigvala{n}@{0} = n^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/28.2.E23 28.2.E23] || <math qid="Q8166">\Mathieueigvala{n}@{0} = n^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/28.2.E24 28.2.E24] || [[Item:Q8167|<math>\Mathieueigvalb{n}@{0} = n^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
+| [https://dlmf.nist.gov/28.2.E24 28.2.E24] || <math qid="Q8167">\Mathieueigvalb{n}@{0} = n^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{n}@{0} = n^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(n, 0) = (n)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[n, 0] == (n)^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
 |-
-| [https://dlmf.nist.gov/28.2.E26 28.2.E26] || [[Item:Q8169|<math>\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n, - q) = MathieuA(2*n, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n, - q] == MathieuCharacteristicA[2*n, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
+| [https://dlmf.nist.gov/28.2.E26 28.2.E26] || <math qid="Q8169">\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n}@{-q} = \Mathieueigvala{2n}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n, - q) = MathieuA(2*n, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n, - q] == MathieuCharacteristicA[2*n, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/28.2.E27 28.2.E27] || [[Item:Q8170|<math>\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n + 1, - q) = MathieuB(2*n + 1, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n + 1, - q] == MathieuCharacteristicB[2*n + 1, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
+| [https://dlmf.nist.gov/28.2.E27 28.2.E27] || <math qid="Q8170">\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvala{2n+1}@{-q} = \Mathieueigvalb{2n+1}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuA(2*n + 1, - q) = MathieuB(2*n + 1, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicA[2*n + 1, - q] == MathieuCharacteristicB[2*n + 1, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/28.2.E28 28.2.E28] || [[Item:Q8171|<math>\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(2*n + 2, - q) = MathieuB(2*n + 2, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[2*n + 2, - q] == MathieuCharacteristicB[2*n + 2, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
+| [https://dlmf.nist.gov/28.2.E28 28.2.E28] || <math qid="Q8171">\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieueigvalb{2n+2}@{-q} = \Mathieueigvalb{2n+2}@{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuB(2*n + 2, - q) = MathieuB(2*n + 2, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuCharacteristicB[2*n + 2, - q] == MathieuCharacteristicB[2*n + 2, q]</syntaxhighlight> || Failure || Failure || Successful [Tested: 30] || Successful [Tested: 30]
 |-
-| [https://dlmf.nist.gov/28.2#Ex4 28.2#Ex4] || [[Item:Q8172|<math>\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(0, 0, z) = 1/(sqrt(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[0, 0, z] == 1/(Sqrt[2])</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 7]
+| [https://dlmf.nist.gov/28.2#Ex4 28.2#Ex4] || <math qid="Q8172">\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{0}@{z}{0} = 1/\sqrt{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(0, 0, z) = 1/(sqrt(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[0, 0, z] == 1/(Sqrt[2])</syntaxhighlight> || Failure || Successful || Skip - No test values generated || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/28.2#Ex5 28.2#Ex5] || [[Item:Q8173|<math>\Mathieuce{n}@{z}{0} = \cos@{nz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{n}@{z}{0} = \cos@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(n, 0, z) = cos(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[n, 0, z] == Cos[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6753267742469401, 0.4379310296367226]
+| [https://dlmf.nist.gov/28.2#Ex5 28.2#Ex5] || <math qid="Q8173">\Mathieuce{n}@{z}{0} = \cos@{nz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{n}@{z}{0} = \cos@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(n, 0, z) = cos(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[n, 0, z] == Cos[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6753267742469401, 0.4379310296367226]
 Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.1123802552186532, 0.12519411502047795]
 Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2#Ex6 28.2#Ex6] || [[Item:Q8174|<math>\Mathieuse{n}@{z}{0} = \sin@{nz}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{n}@{z}{0} = \sin@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(n, 0, z) = sin(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[n, 0, z] == Sin[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.17898073764673827, 1.8916506821927568]
+| [https://dlmf.nist.gov/28.2#Ex6 28.2#Ex6] || <math qid="Q8174">\Mathieuse{n}@{z}{0} = \sin@{nz}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{n}@{z}{0} = \sin@{nz}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(n, 0, z) = sin(n*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[n, 0, z] == Sin[n*z]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.17898073764673827, 1.8916506821927568]
 Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[4.947243351054952, 0.9068272427732345]
 Test Values: {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2#Ex7 28.2#Ex7] || [[Item:Q8175|<math>\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuCE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[6.9214963829238805, 34.195194735367046]
+| [https://dlmf.nist.gov/28.2#Ex7 28.2#Ex7] || <math qid="Q8175">\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuce{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuCE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuC[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[6.9214963829238805, 34.195194735367046]
 Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.5092269783308243, -0.4627812517943034]
 Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2#Ex8 28.2#Ex8] || [[Item:Q8176|<math>\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuSE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.15495486e-1+.3109277201e-1*I
+| [https://dlmf.nist.gov/28.2#Ex8 28.2#Ex8] || <math qid="Q8176">\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\left(\Mathieuse{n}@{x}{q}\right)^{2}\diff{x} = \pi</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((MathieuSE(n, q, x))^(2), x = 0..2*Pi) = Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(MathieuS[n, q, x])^(2), {x, 0, 2*Pi}, GenerateConditions->None] == Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.15495486e-1+.3109277201e-1*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.592260336+2.720760990*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-11.13627493115099, -34.66471446201499]
@@ Line 62: / Line 62: @@
 Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2.E31 28.2.E31] || [[Item:Q8177|<math>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuCE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuC[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/28.2.E31 28.2.E31] || <math qid="Q8177">\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuce{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuCE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuC[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/28.2.E32 28.2.E32] || [[Item:Q8178|<math>\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuSE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuS[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/28.2.E32 28.2.E32] || <math qid="Q8178">\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuse{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math>n \neq m</math> || <syntaxhighlight lang=mathematica>int(MathieuSE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuS[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/28.2.E33 28.2.E33] || [[Item:Q8179|<math>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
+| [https://dlmf.nist.gov/28.2.E33 28.2.E33] || <math qid="Q8179">\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{2\pi}\Mathieuce{m}@{x}{q}\Mathieuse{n}@{x}{q}\diff{x} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(MathieuCE(m, q, x)*MathieuSE(n, q, x), x = 0..2*Pi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[MathieuC[m, q, x]*MathieuS[n, q, x], {x, 0, 2*Pi}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/28.2.E34 28.2.E34] || [[Item:Q8180|<math>\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n, - q, z) = (- 1)^(n)* MathieuCE(2*n, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n, - q, z] == (- 1)^(n)* MathieuC[2*n, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.40308591506050084, 0.46785287118948815]
+| [https://dlmf.nist.gov/28.2.E34 28.2.E34] || <math qid="Q8180">\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n}@{z}{-q} = (-1)^{n}\Mathieuce{2n}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n, - q, z) = (- 1)^(n)* MathieuCE(2*n, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n, - q, z] == (- 1)^(n)* MathieuC[2*n, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.40308591506050084, 0.46785287118948815]
 Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.60084404002985, 1.182666432116677]
 Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2.E35 28.2.E35] || [[Item:Q8181|<math>\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n + 1, - q, z) = (- 1)^(n)* MathieuSE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n + 1, - q, z] == (- 1)^(n)* MathieuS[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.5024747894079764, -2.6392504264802374]
+| [https://dlmf.nist.gov/28.2.E35 28.2.E35] || <math qid="Q8181">\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuce{2n+1}@{z}{-q} = (-1)^{n}\Mathieuse{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuCE(2*n + 1, - q, z) = (- 1)^(n)* MathieuSE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuC[2*n + 1, - q, z] == (- 1)^(n)* MathieuS[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.5024747894079764, -2.6392504264802374]
 Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.189026591129222, 0.3274807845663039]
 Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2.E36 28.2.E36] || [[Item:Q8182|<math>\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 1, - q, z) = (- 1)^(n)* MathieuCE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 1, - q, z] == (- 1)^(n)* MathieuC[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.280260494012772, -3.1853558239364403]
+| [https://dlmf.nist.gov/28.2.E36 28.2.E36] || <math qid="Q8182">\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+1}@{z}{-q} = (-1)^{n}\Mathieuce{2n+1}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 1, - q, z) = (- 1)^(n)* MathieuCE(2*n + 1, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 1, - q, z] == (- 1)^(n)* MathieuC[2*n + 1, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 210] || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.280260494012772, -3.1853558239364403]
 Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.634104542197209, -1.1703184896606507]
 Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/28.2.E37 28.2.E37] || [[Item:Q8183|<math>\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 2, - q, z) = (- 1)^(n)* MathieuSE(2*n + 2, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 2, - q, z] == (- 1)^(n)* MathieuS[2*n + 2, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3430671662+7.821986266*I
+| [https://dlmf.nist.gov/28.2.E37 28.2.E37] || <math qid="Q8183">\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Mathieuse{2n+2}@{z}{-q} = (-1)^{n}\Mathieuse{2n+2}@{\tfrac{1}{2}\pi-z}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>MathieuSE(2*n + 2, - q, z) = (- 1)^(n)* MathieuSE(2*n + 2, q, (1)/(2)*Pi - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>MathieuS[2*n + 2, - q, z] == (- 1)^(n)* MathieuS[2*n + 2, q, Divide[1,2]*Pi - z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3430671662+7.821986266*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 20.99712460-1.294028748*I
 Test Values: {q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.02456715747845, -1.021331524922309]

28.2: Difference between revisions

Latest revision as of 12:07, 28 June 2021

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