View source for 32.11

{{DISPLAYTITLE:Painlevé Transcendents - 32.11 Asymptotic Approximations for Real Variables}}

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/32.11.E2 32.11.E2] || <math qid="Q9437">\phi(x) = (24)^{1/4}\left(\tfrac{4}{5}|x|^{5/4}-\tfrac{5}{8}d^{2}\ln@@{|x|}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = (24)^{1/4}\left(\tfrac{4}{5}|x|^{5/4}-\tfrac{5}{8}d^{2}\ln@@{|x|}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = (24)^(1/4)*((4)/(5)*(abs(x))^(5/4)-(5)/(8)*(d)^(2)* ln(abs(x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == (24)^(1/4)*(Divide[4,5]*(Abs[x])^(5/4)-Divide[5,8]*(d)^(2)* Log[Abs[x]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.359899020+1.235754628*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7909045934-.5804030210*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.3598990205302544, 1.2357546278215892]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.408937126206912, 1.7847927334982474]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E7 32.11.E7] || <math qid="Q9442">\phi(x) = \tfrac{2}{3}|x|^{3/2}-\tfrac{3}{4}d^{2}\ln@@{|x|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = \tfrac{2}{3}|x|^{3/2}-\tfrac{3}{4}d^{2}\ln@@{|x|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = (2)/(3)*(abs(x))^(3/2)-(3)/(4)*(d)^(2)* ln(abs(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == Divide[2,3]*(Abs[x])^(3/2)-Divide[3,4]*(d)^(2)* Log[Abs[x]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2263426496+1.013357313*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.626197514e-1-.2002123003*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.22634264982563074, 1.0133573129774054]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.8226954558510269, 1.5623954186540636]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E8 32.11.E8] || <math qid="Q9443">d^{2} = -\pi^{-1}\ln@{1-k^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d^{2} = -\pi^{-1}\ln@{1-k^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(d)^(2) = - (Pi)^(- 1)* ln(1 - (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(d)^(2) == - (Pi)^(- 1)* Log[1 - (k)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(-infinity)+.8660254040*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8496991530+1.866025404*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[-1]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.84969915256606, 1.8660254037844386]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E9 32.11.E9] || <math qid="Q9444">\theta_{0} = \tfrac{3}{2}d^{2}\ln@@{2}+\phase@@{\EulerGamma@{1-\tfrac{1}{2}id^{2}}}+\tfrac{1}{4}\pi(1-2\sign@{k})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\theta_{0} = \tfrac{3}{2}d^{2}\ln@@{2}+\phase@@{\EulerGamma@{1-\tfrac{1}{2}id^{2}}}+\tfrac{1}{4}\pi(1-2\sign@{k})</syntaxhighlight> || <math>\realpart@@{(1-\tfrac{1}{2}\iunit d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>theta[0] = (3)/(2)*(d)^(2)* ln(2)+ argument(GAMMA(1 -(1)/(2)*I*(d)^(2)))+(1)/(4)*Pi*(1 - 2*signum(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Theta], 0] == Divide[3,2]*(d)^(2)* Log[2]+ Arg[Gamma[1 -Divide[1,2]*I*(d)^(2)]]+Divide[1,4]*Pi*(1 - 2*Sign[k])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.126938891-.4004246008*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.126938891-.4004246008*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.1269388909194178, -0.4004246003897078]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1269388909194178, -0.4004246003897078]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E14 32.11.E14] || <math qid="Q9449">\phi(x) = \tfrac{2}{3}|x|^{3/2}+\tfrac{3}{4}d^{2}\ln@@{|x|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = \tfrac{2}{3}|x|^{3/2}+\tfrac{3}{4}d^{2}\ln@@{|x|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = (2)/(3)*(abs(x))^(3/2)+(3)/(4)*(d)^(2)* ln(abs(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == Divide[2,3]*(Abs[x])^(3/2)+Divide[3,4]*(d)^(2)* Log[Abs[x]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.777561816e-1+.4866426869*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4572406346+.7002123003*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.0777561812554926, 0.48664268702259433]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.1267942869321503, 1.0356807926992524]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E15 32.11.E15] || <math qid="Q9450">\chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} = n\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} = n\pi</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2}\iunit d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) = n*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] == n*Pi</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.109048867-.4004246008*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -7.250641521-.4004246008*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-4.10904886506357, -0.4004246003897078]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 1], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-7.250641518653364, -0.4004246003897078]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 2], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E17 32.11.E17] || <math qid="Q9452">d^{2} = \pi^{-1}\ln@{1+k^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d^{2} = \pi^{-1}\ln@{1+k^{2}}</syntaxhighlight> || <math>\sign@{k} = (-1)^{n}</math> || <syntaxhighlight lang=mathematica>(d)^(2) = (Pi)^(- 1)* ln(1 + (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(d)^(2) == (Pi)^(- 1)* Log[1 + (k)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2793644003+.8660254040*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.122999981e-1+.8660254040*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2793643998473485, 0.8660254037844386]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.012299998726776007, 0.8660254037844386]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E18 32.11.E18] || <math qid="Q9453">\chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} \neq n\pi</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\chi+\tfrac{3}{2}d^{2}\ln@@{2}-\tfrac{1}{4}\pi-\phase@@{\EulerGamma@{\tfrac{1}{2}id^{2}}} \neq n\pi</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2}\iunit d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) <> n*Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] \[NotEqual]n*Pi</syntaxhighlight> || Failure || Failure || Successful [Tested: 60] || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 1.0]]]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 1], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 2.0]]]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[n, 2], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E20 32.11.E20] || <math qid="Q9455">\psi(x) = \tfrac{2}{3}\sqrt{2}x^{3/2}-\tfrac{3}{2}\rho^{2}\ln@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\psi(x) = \tfrac{2}{3}\sqrt{2}x^{3/2}-\tfrac{3}{2}\rho^{2}\ln@@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>psi(x) = (2)/(3)*sqrt(2)*(x)^(3/2)-(3)/(2)*(rho)^(2)* ln(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Psi][x] == Divide[2,3]*Sqrt[2]*(x)^(3/2)-Divide[3,2]*\[Rho]^(2)* Log[x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1289138697+1.276714626*I
Test Values: {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4201810172-.6504246006*I
Test Values: {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.12891387081109584, 1.276714625954811]
Test Values: {Rule[x, 1.5], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.1779519764877535, 1.8257527316314692]
Test Values: {Rule[x, 1.5], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ψ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E21 32.11.E21] || <math qid="Q9456">\sigma = -\sign@{\imagpart@@{s}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sigma = -\sign@{\imagpart@@{s}}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2}\iunit d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>sigma = - signum(Im((exp(Pi*(d)^(2))- 1)^(1/2)* exp(I*((3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi + chi - argument(GAMMA((1)/(2)*I*(d)^(2)))))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Sigma] == - Sign[Im[(Exp[Pi*(d)^(2)]- 1)^(1/2)* Exp[I*(Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi + \[Chi]- Arg[Gamma[Divide[1,2]*I*(d)^(2)]])]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1339745960+.5000000000*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), sigma = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.500000000+.8660254040*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), sigma = -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 [200 / 200]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.1339745962155613, 0.49999999999999994]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844388, 0.49999999999999994]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E22 32.11.E22] || <math qid="Q9457">\rho^{2} = \pi^{-1}\ln@{(1+|s|^{2})/|2\imagpart@@{s}|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\rho^{2} = \pi^{-1}\ln@{(1+|s|^{2})/|2\imagpart@@{s}|}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2}\iunit d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>(rho)^(2) = (Pi)^(- 1)* ln((1 +(abs((exp(Pi*(d)^(2))- 1)^(1/2)* exp(I*((3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi + chi - argument(GAMMA((1)/(2)*I*(d)^(2)))))))^(2))/abs(2*Im((exp(Pi*(d)^(2))- 1)^(1/2)* exp(I*((3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi + chi - argument(GAMMA((1)/(2)*I*(d)^(2))))))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Rho]^(2) == (Pi)^(- 1)* Log[(1 +(Abs[(Exp[Pi*(d)^(2)]- 1)^(1/2)* Exp[I*(Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi + \[Chi]- Arg[Gamma[Divide[1,2]*I*(d)^(2)]])]])^(2))/Abs[2*Im[(Exp[Pi*(d)^(2)]- 1)^(1/2)* Exp[I*(Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi + \[Chi]- Arg[Gamma[Divide[1,2]*I*(d)^(2)]])]]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2989013521+.8660254040*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), rho = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7010986487-.8660254040*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), rho = -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 [200 / 200]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2989013519411052, 0.8660254037844386]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.3675975407110632, 0.8660254037844386]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E23 32.11.E23] || <math qid="Q9458">\theta = -\tfrac{3}{4}\pi-\tfrac{7}{2}\rho^{2}\ln{2}+\phase@{1+s^{2}}+\phase@@{\EulerGamma@{i\rho^{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\theta = -\tfrac{3}{4}\pi-\tfrac{7}{2}\rho^{2}\ln{2}+\phase@{1+s^{2}}+\phase@@{\EulerGamma@{i\rho^{2}}}</syntaxhighlight> || <math>\realpart@@{(\iunit \rho^{2})} > 0</math> || <syntaxhighlight lang=mathematica>theta = -(3)/(4)*Pi -(7)/(2)*(rho)^(2)* ln(2)+ argument(1 +((exp(Pi*(d)^(2))- 1)^(1/2)* exp(I*((3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi + chi - argument(GAMMA((1)/(2)*I*(d)^(2))))))^(2))+ argument(GAMMA(I*(rho)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Theta] == -Divide[3,4]*Pi -Divide[7,2]*\[Rho]^(2)* Log[2]+ Arg[1 +((Exp[Pi*(d)^(2)]- 1)^(1/2)* Exp[I*(Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi + \[Chi]- Arg[Gamma[Divide[1,2]*I*(d)^(2)]])])^(2)]+ Arg[Gamma[I*\[Rho]^(2)]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.925696688-1.600990735*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = 1/2*3^(1/2)+1/2*I, rho = -1/2+1/2*I*3^(1/2), theta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5596712830-1.234965331*I
Test Values: {chi = 1/2*3^(1/2)+1/2*I, d = 1/2*3^(1/2)+1/2*I, rho = -1/2+1/2*I*3^(1/2), theta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6978889663556802, -1.6009907342426515]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.496658442211441, -1.6009907342426515]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[χ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E27 32.11.E27] || <math qid="Q9462">\sigma = (2/\pi)\asin@{\pi\lambda}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sigma = (2/\pi)\asin@{\pi\lambda}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sigma = (2/Pi)*arcsin(Pi*lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Sigma] == (2/Pi)*ArcSin[Pi*\[Lambda]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2138525505-.6623078870*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.152172854-.2962824830*I
Test Values: {lambda = 1/2*3^(1/2)+1/2*I, sigma = -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 [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2138525499640901, -0.6623078873679977]
Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.1521728538203484, -0.296282483583559]
Test Values: {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E28 32.11.E28] || <math qid="Q9463">B = 2^{-2\sigma}\frac{\EulerGamma^{2}@{\tfrac{1}{2}(1-\sigma)}\EulerGamma@{\tfrac{1}{2}(1+\sigma)+\nu}}{\EulerGamma^{2}@{\tfrac{1}{2}(1+\sigma)}\EulerGamma@{\tfrac{1}{2}(1-\sigma)+\nu}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>B = 2^{-2\sigma}\frac{\EulerGamma^{2}@{\tfrac{1}{2}(1-\sigma)}\EulerGamma@{\tfrac{1}{2}(1+\sigma)+\nu}}{\EulerGamma^{2}@{\tfrac{1}{2}(1+\sigma)}\EulerGamma@{\tfrac{1}{2}(1-\sigma)+\nu}}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2}(1-\sigma))} > 0, \realpart@@{(\tfrac{1}{2}(1+\sigma)+\nu)} > 0, \realpart@@{(\tfrac{1}{2}(1+\sigma))} > 0, \realpart@@{(\tfrac{1}{2}(1-\sigma)+\nu)} > 0</math> || <syntaxhighlight lang=mathematica>B = (2)^(- 2*sigma)*((GAMMA((1)/(2)*(1 - sigma)))^(2)* GAMMA((1)/(2)*(1 + sigma)+ nu))/((GAMMA((1)/(2)*(1 + sigma)))^(2)* GAMMA((1)/(2)*(1 - sigma)+ nu))</syntaxhighlight> || <syntaxhighlight lang=mathematica>B == (2)^(- 2*\[Sigma])*Divide[(Gamma[Divide[1,2]*(1 - \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 + \[Sigma])+ \[Nu]],(Gamma[Divide[1,2]*(1 + \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 - \[Sigma])+ \[Nu]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.808977659-.2371191295*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9147008442+.353764288e-1*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, sigma = -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[3.808977656026658, -0.23711913260929035]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.914700843688173, 0.035376428936519655]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E31 32.11.E31] || <math qid="Q9466">h^{*} = \ifrac{1}{\left(\pi^{1/2}\EulerGamma@{\nu+1}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>h^{*} = \ifrac{1}{\left(\pi^{1/2}\EulerGamma@{\nu+1}\right)}</syntaxhighlight> || <math>\realpart@@{(\nu+1)} > 0</math> || <syntaxhighlight lang=mathematica>(h)^(*) = (1)/((Pi)^(1/2)* GAMMA(nu + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(h)^(*) == Divide[1,(Pi)^(1/2)* Gamma[\[Nu]+ 1]]</syntaxhighlight> || Error || Failure || - || Error
|- 
| [https://dlmf.nist.gov/32.11.E34 32.11.E34] || <math qid="Q9469">\phi(x) = \tfrac{1}{3}\sqrt{3}x^{2}-\tfrac{4}{3}d^{2}\sqrt{3}\ln@{\sqrt{2}|x|}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = \tfrac{1}{3}\sqrt{3}x^{2}-\tfrac{4}{3}d^{2}\sqrt{3}\ln@{\sqrt{2}|x|}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = (1)/(3)*sqrt(3)*(x)^(2)-(4)/(3)*(d)^(2)*sqrt(3)*ln(sqrt(2)*abs(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == Divide[1,3]*Sqrt[3]*(x)^(2)-Divide[4,3]*(d)^(2)*Sqrt[3]*Log[Sqrt[2]*Abs[x]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8683794902+2.254077396*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1115135772-.4431471813*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8683794899108137, 2.2540773967762746]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.180658615765844, 2.8031155024529326]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E35 32.11.E35] || <math qid="Q9470">d^{2} = -\tfrac{1}{4}\sqrt{3}\pi^{-1}\ln@{1-|\mu|^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d^{2} = -\tfrac{1}{4}\sqrt{3}\pi^{-1}\ln@{1-|\mu|^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(d)^(2) = -(1)/(4)*sqrt(3)*(Pi)^(- 1)* ln(1 -(abs(mu))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(d)^(2) == -Divide[1,4]*Sqrt[3]*(Pi)^(- 1)* Log[1 -(Abs[\[Mu]])^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(-infinity)+.8660254040*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(-infinity)+.8660254040*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, mu = -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 [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[-1]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: DirectedInfinity[-1]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E36 32.11.E36] || <math qid="Q9471">\theta_{0} = \tfrac{1}{3}d^{2}\sqrt{3}\ln@@{3}+\tfrac{2}{3}\pi\nu+\tfrac{7}{12}\pi+\phase@@{\mu}+\phase@@{\EulerGamma@{-\tfrac{2}{3}i\sqrt{3}d^{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\theta_{0} = \tfrac{1}{3}d^{2}\sqrt{3}\ln@@{3}+\tfrac{2}{3}\pi\nu+\tfrac{7}{12}\pi+\phase@@{\mu}+\phase@@{\EulerGamma@{-\tfrac{2}{3}i\sqrt{3}d^{2}}}</syntaxhighlight> || <math>\realpart@@{(-\tfrac{2}{3}\iunit \sqrt{3}d^{2})} > 0</math> || <syntaxhighlight lang=mathematica>theta[0] = (1)/(3)*(d)^(2)*sqrt(3)*ln(3)+(2)/(3)*Pi*nu +(7)/(12)*Pi + argument(mu)+ argument(GAMMA(-(2)/(3)*I*sqrt(3)*(d)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Theta], 0] == Divide[1,3]*(d)^(2)*Sqrt[3]*Log[3]+Divide[2,3]*Pi*\[Nu]+Divide[7,12]*Pi + Arg[\[Mu]]+ Arg[Gamma[-Divide[2,3]*I*Sqrt[3]*(d)^(2)]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.888102442-1.096503697*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -5.254127846-.7304782927*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, theta[0] = -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[-3.888102439563878, -1.0965036955306524]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-5.254127843348316, -0.7304782917462136]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[θ, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/32.11.E37 32.11.E37] || <math qid="Q9472">\mu = 1+\left(\ifrac{2ih\pi^{3/2}\exp@{-i\pi\nu}}{\EulerGamma@{-\nu}}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu = 1+\left(\ifrac{2ih\pi^{3/2}\exp@{-i\pi\nu}}{\EulerGamma@{-\nu}}\right)</syntaxhighlight> || <math>\realpart@@{(-\nu)} > 0</math> || <syntaxhighlight lang=mathematica>mu = 1 +((2*I*h*(Pi)^(3/2)* exp(- I*Pi*nu))/(GAMMA(- nu)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu] == 1 +(Divide[2*I*h*(Pi)^(3/2)* Exp[- I*Pi*\[Nu]],Gamma[- \[Nu]]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 241.2310915-105.5149067*I
Test Values: {h = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.289758519+2.890481636*I
Test Values: {h = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, nu = -1/2*3^(1/2)-1/2*I}</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[241.23109103950634, -105.514906477147]
Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.289758518042884, 2.89048163412207]
Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|}
</div>