Results of Painlevé Transcendents: Difference between revisions

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{| class="wikitable sortable" style="margin: 0;"
; Notation : [[32.1|32.1 Special Notation]]<br>
|-
; Properties : [[32.2|32.2 Differential Equations]]<br>[[32.3|32.3 Graphics]]<br>[[32.4|32.4 Isomonodromy Problems]]<br>[[32.5|32.5 Integral Equations]]<br>[[32.6|32.6 Hamiltonian Structure]]<br>[[32.7|32.7 Bäcklund Transformations]]<br>[[32.8|32.8 Rational Solutions]]<br>[[32.9|32.9 Other Elementary Solutions]]<br>[[32.10|32.10 Special Function Solutions]]<br>[[32.11|32.11 Asymptotic Approximations for Real Variables]]<br>[[32.12|32.12 Asymptotic Approximations for Complex Variables]]<br>
! scope="col" style="position: sticky; top: 0;" | DLMF
; Applications : [[32.13|32.13 Reductions of Partial Differential Equations]]<br>[[32.14|32.14 Combinatorics]]<br>[[32.15|32.15 Orthogonal Polynomials]]<br>[[32.16|32.16 Physical Applications]]<br>
! scope="col" style="position: sticky; top: 0;" | Formula
; Computation : [[32.17|32.17 Methods of Computation]]<br>
! scope="col" style="position: sticky; top: 0;" | Constraints
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-
| [https://dlmf.nist.gov/32.2.E1 32.2.E1] || [[Item:Q9154|<math>\deriv[2]{w}{z} = 6w^{2}+z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = 6w^{2}+z</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = 6*(w)^(2)+ z</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == 6*(w)^(2)+ z</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.866025406-5.696152424*I
Test Values: {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.500000002-6.062177828*I
Test Values: {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.8660254037844397, -5.696152422706632]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.500000000000001, -6.06217782649107]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E2 32.2.E2] || [[Item:Q9155|<math>\deriv[2]{w}{z} = 2w^{3}+zw+\alpha</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = 2w^{3}+zw+\alpha</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = 2*(w)^(3)+ z*w + alpha</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == 2*(w)^(3)+ z*w + \[Alpha]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [209 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.000000001-2.866025406*I
Test Values: {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6339745966-2.500000002*I
Test Values: {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [209 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.0, -2.8660254037844384]
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[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.0, -2.8660254037844384]
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[α, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E3 32.2.E3] || [[Item:Q9156|<math>\deriv[2]{w}{z} = \frac{1}{w}\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{\alpha w^{2}+\beta}{z}+\gamma w^{3}+\frac{\delta}{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = \frac{1}{w}\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{\alpha w^{2}+\beta}{z}+\gamma w^{3}+\frac{\delta}{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = (1)/(w)*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+(alpha*(w)^(2)+ beta)/(z)+ gamma*(w)^(3)+(delta)/(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == Divide[1,w]*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[\[Alpha]*(w)^(2)+ \[Beta],z]+ \[Gamma]*(w)^(3)+Divide[\[Delta],w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.598076212-.5772156656*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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: -1.000000000+2.020860546*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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 [299 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.098076211353316, -0.8660254037844389]
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.098076211353316, -1.8660254037844388]
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E4 32.2.E4] || [[Item:Q9157|<math>\deriv[2]{w}{z} = \frac{1}{2w}\left(\deriv{w}{z}\right)^{2}+\frac{3}{2}w^{3}+4zw^{2}+2(z^{2}-\alpha)w+\frac{\beta}{w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = \frac{1}{2w}\left(\deriv{w}{z}\right)^{2}+\frac{3}{2}w^{3}+4zw^{2}+2(z^{2}-\alpha)w+\frac{\beta}{w}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = (1)/(2*w)*(diff(w, z))^(2)+(3)/(2)*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- alpha)*w +(beta)/(w)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == Divide[1,2*w]*(D[w, z])^(2)+Divide[3,2]*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- \[Alpha])*w +Divide[\[Beta],w]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.299038104-5.250000007*I
Test Values: {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 5.299038110+2.749999997*I
Test Values: {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2990381056766576, -5.25]
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[α, 1.5], Rule[β, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.1650635094610964, -5.75]
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[α, 1.5], Rule[β, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E5 32.2.E5] || [[Item:Q9158|<math>\deriv[2]{w}{z} = \left(\frac{1}{2w}+\frac{1}{w-1}\right)\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{(w-1)^{2}}{z^{2}}\left(\alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = \left(\frac{1}{2w}+\frac{1}{w-1}\right)\left(\deriv{w}{z}\right)^{2}-\frac{1}{z}\deriv{w}{z}+\frac{(w-1)^{2}}{z^{2}}\left(\alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = ((1)/(2*w)+(1)/(w - 1))*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+((w - 1)^(2))/((z)^(2))*(alpha*w +(beta)/(w))+(gamma*w)/(z)+(delta*w*(w + 1))/(w - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == (Divide[1,2*w]+Divide[1,w - 1])*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[(w - 1)^(2),(z)^(2)]*(\[Alpha]*w +Divide[\[Beta],w])+Divide[\[Gamma]*w,z]+Divide[\[Delta]*w*(w + 1),w - 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.206380793+1.517949194*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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: -3.834936494+2.791317281*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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[-3.495190528383291, 1.017949192431124]
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.1291651245988517, -4.0801270189221945]
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E6 32.2.E6] || [[Item:Q9159|<math>\deriv[2]{w}{z} = \frac{1}{2}\left(\frac{1}{w}+\frac{1}{w-1}+\frac{1}{w-z}\right)\left(\deriv{w}{z}\right)^{2}-\left(\frac{1}{z}+\frac{1}{z-1}+\frac{1}{w-z}\right)\deriv{w}{z}+\frac{w(w-1)(w-z)}{z^{2}(z-1)^{2}}\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+\frac{\delta z(z-1)}{(w-z)^{2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = \frac{1}{2}\left(\frac{1}{w}+\frac{1}{w-1}+\frac{1}{w-z}\right)\left(\deriv{w}{z}\right)^{2}-\left(\frac{1}{z}+\frac{1}{z-1}+\frac{1}{w-z}\right)\deriv{w}{z}+\frac{w(w-1)(w-z)}{z^{2}(z-1)^{2}}\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+\frac{\delta z(z-1)}{(w-z)^{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = (1)/(2)*((1)/(w)+(1)/(w - 1)+(1)/(w - z))*(diff(w, z))^(2)-((1)/(z)+(1)/(z - 1)+(1)/(w - z))*diff(w, z)+(w*(w - 1)*(w - z))/((z)^(2)*(z - 1)^(2))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta*z*(z - 1))/((w - z)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == Divide[1,2]*(Divide[1,w]+Divide[1,w - 1]+Divide[1,w - z])*(D[w, z])^(2)-(Divide[1,z]+Divide[1,z - 1]+Divide[1,w - z])*D[w, z]+Divide[w*(w - 1)*(w - z),(z)^(2)*(z - 1)^(2)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+Divide[\[Delta]*z*(z - 1),(w - z)^(2)])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [269 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9380246356e-1+1.316803425*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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><syntaxhighlight lang=mathematica>Result: 1.739453154+1.182694224*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 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: Indeterminate
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex1 32.2#Ex1] || [[Item:Q9161|<math>W(\zeta) = \frac{a(z)w+b(z)}{c(z)w+d(z)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>W(\zeta) = \frac{a(z)w+b(z)}{c(z)w+d(z)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W(zeta) = (a(z)* w + b(z))/(c(z)* w + d(z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W[\[Zeta]] == Divide[a[z]* w + b[z],c[z]* w + d[z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex2 32.2#Ex2] || [[Item:Q9162|<math>\zeta = \phi(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta = \phi(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta = phi(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta] == \[Phi][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.2.E9 32.2.E9] || [[Item:Q9163|<math>\deriv[2]{u}{\zeta} = \frac{1}{u}\left(\deriv{u}{\zeta}\right)^{2}-\frac{1}{\zeta}\deriv{u}{\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}+\frac{\beta}{4\zeta}+\frac{\delta}{4u}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u}{\zeta} = \frac{1}{u}\left(\deriv{u}{\zeta}\right)^{2}-\frac{1}{\zeta}\deriv{u}{\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}+\frac{\beta}{4\zeta}+\frac{\delta}{4u}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u, [zeta$(2)]) = (1)/(u)*(diff(u, zeta))^(2)-(1)/(zeta)*diff(u, zeta)+((u)^(2)*(alpha + gamma*u))/(4*(zeta)^(2))+(beta)/(4*zeta)+(delta)/(4*u)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[u, {\[Zeta], 2}] == Divide[1,u]*(D[u, \[Zeta]])^(2)-Divide[1,\[Zeta]]*D[u, \[Zeta]]+Divide[(u)^(2)*(\[Alpha]+ \[Gamma]*u),4*\[Zeta]^(2)]+Divide[\[Beta],4*\[Zeta]]+Divide[\[Delta],4*u]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.074730384+.1153480418*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4374708571+.3969114845*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0747595264191645, -0.029006350946109677]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4374999999999999, 0.541265877365274]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E10 32.2.E10] || [[Item:Q9164|<math>\deriv[2]{u}{z}+\frac{1}{z}\deriv{u}{z} = \frac{2\alpha}{z}\sin@@{u}+2\gamma\sin@{2u}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u}{z}+\frac{1}{z}\deriv{u}{z} = \frac{2\alpha}{z}\sin@@{u}+2\gamma\sin@{2u}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u, [z$(2)])+(1)/(z)*diff(u, z) = (2*alpha)/(z)*sin(u)+ 2*gamma*sin(2*u)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[u, {z, 2}]+Divide[1,z]*D[u, z] == Divide[2*\[Alpha],z]*Sin[u]+ 2*\[Gamma]*Sin[2*u]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.496361213+.6291944644*I
Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.346900984+2.955916370*I
Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, u = 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[-5.5647975539874, -0.7848783935570325]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.5418435125289267, -2.4153373252737342]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E11 32.2.E11] || [[Item:Q9165|<math>\deriv[2]{u}{\zeta} = 3u^{5}+2\zeta u^{3}+\left(\tfrac{1}{4}\zeta^{2}-\nu-\tfrac{1}{2}\right)u+\frac{\beta}{32u^{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u}{\zeta} = 3u^{5}+2\zeta u^{3}+\left(\tfrac{1}{4}\zeta^{2}-\nu-\tfrac{1}{2}\right)u+\frac{\beta}{32u^{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u, [zeta$(2)]) = 3*(u)^(5)+ 2*zeta*(u)^(3)+((1)/(4)*(zeta)^(2)- nu -(1)/(2))*u +(beta)/(32*(u)^(3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[u, {\[Zeta], 2}] == 3*(u)^(5)+ 2*\[Zeta]*(u)^(3)+(Divide[1,4]*\[Zeta]^(2)- \[Nu]-Divide[1,2])*u +Divide[\[Beta],32*(u)^(3)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.531088915-2.319150408*I
Test Values: {beta = 3/2, nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 5.263139725+.9129004010*I
Test Values: {beta = 3/2, nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.531088913245536, -2.3191504037844384]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.165063509461097, -2.685175807568877]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[ζ, 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/32.2.E12 32.2.E12] || [[Item:Q9166|<math>\deriv[2]{u}{\zeta} = -\frac{\alpha\cosh@@{u}}{2(\sinh@@{u})^{3}}-\frac{\beta\sinh@@{u}}{2(\cosh@@{u})^{3}}-\tfrac{1}{4}\gamma e^{\zeta}\sinh@{2u}-\tfrac{1}{8}\delta e^{2\zeta}\sinh@{4u}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u}{\zeta} = -\frac{\alpha\cosh@@{u}}{2(\sinh@@{u})^{3}}-\frac{\beta\sinh@@{u}}{2(\cosh@@{u})^{3}}-\tfrac{1}{4}\gamma e^{\zeta}\sinh@{2u}-\tfrac{1}{8}\delta e^{2\zeta}\sinh@{4u}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u, [zeta$(2)]) = -(alpha*cosh(u))/(2*(sinh(u))^(3))-(beta*sinh(u))/(2*(cosh(u))^(3))-(1)/(4)*gamma*exp(zeta)*sinh(2*u)-(1)/(8)*delta*exp(2*zeta)*sinh(4*u)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[u, {\[Zeta], 2}] == -Divide[\[Alpha]*Cosh[u],2*(Sinh[u])^(3)]-Divide[\[Beta]*Sinh[u],2*(Cosh[u])^(3)]-Divide[1,4]*\[Gamma]*Exp[\[Zeta]]*Sinh[2*u]-Divide[1,8]*\[Delta]*Exp[2*\[Zeta]]*Sinh[4*u]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -10.15437375-4.132059394*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1182986371-1.333346640*I
Test Values: {alpha = 3/2, beta = 3/2, delta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-10.983749451492802, -3.604532198424999]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3640397236276506, -1.2834088930332135]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2.E13 32.2.E13] || [[Item:Q9167|<math>z(1-z)I\left(\int_{\infty}^{w}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}\right) = \sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z(1-z)I\left(\int_{\infty}^{w}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}\right) = \sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*(1 - z)*I(int((1)/(sqrt(t*(t - 1)*(t - z))), t = infinity..w)) = sqrt(w*(w - 1)*(w - z))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta -(1)/(2))*(z*(z - 1))/((w - z)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*(1 - z)*I[(Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, Infinity, w}, GenerateConditions->None]) ] == Sqrt[w*(w - 1)*(w - z)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+(\[Delta]-Divide[1,2])*Divide[z*(z - 1),(w - z)^(2)])</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.2.E14 32.2.E14] || [[Item:Q9168|<math>I = z(1-z)\deriv[2]{}{z}+(1-2z)\deriv{}{z}-\frac{1}{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>I = z(1-z)\deriv[2]{}{z}+(1-2z)\deriv{}{z}-\frac{1}{4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>I = z*(1 - z)*diff(+(1 - 2*z)*diff(-, z), [z$(2)])(1)/(4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>I == z*(1 - z)*D[+(1 - 2*z)*D[-, z], {z, 2}]Divide[1,4]</syntaxhighlight> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/32.2#Ex3 32.2#Ex3] || [[Item:Q9169|<math>\deriv{f_{1}}{z}+f_{1}(f_{2}-f_{3})+2\mu_{1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{f_{1}}{z}+f_{1}(f_{2}-f_{3})+2\mu_{1} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f[1], z)+ f[1]*(f[2]- f[3])+ 2*mu[1] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[f, 1], z]+ Subscript[f, 1]*(Subscript[f, 2]- Subscript[f, 3])+ 2*Subscript[\[Mu], 1] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.732050808+1.000000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.000000000+1.732050808*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7320508075688774, 0.9999999999999999]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.9999999999999996, 1.7320508075688774]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2#Ex4 32.2#Ex4] || [[Item:Q9170|<math>\deriv{f_{2}}{z}+f_{2}(f_{3}-f_{1})+2\mu_{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{f_{2}}{z}+f_{2}(f_{3}-f_{1})+2\mu_{2} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f[2], z)+ f[2]*(f[3]- f[1])+ 2*mu[2] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[f, 2], z]+ Subscript[f, 2]*(Subscript[f, 3]- Subscript[f, 1])+ 2*Subscript[\[Mu], 2] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.732050808+1.000000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.000000000+1.732050808*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7320508075688774, 0.9999999999999999]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.9999999999999996, 1.7320508075688774]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.2#Ex5 32.2#Ex5] || [[Item:Q9171|<math>\deriv{f_{3}}{z}+f_{3}(f_{1}-f_{2})+2\mu_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{f_{3}}{z}+f_{3}(f_{1}-f_{2})+2\mu_{3} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(f[3], z)+ f[3]*(f[1]- f[2])+ 2*mu[3] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[f, 3], z]+ Subscript[f, 3]*(Subscript[f, 1]- Subscript[f, 2])+ 2*Subscript[\[Mu], 3] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.732050808+1.000000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.000000000+1.732050808*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7320508075688774, 0.9999999999999999]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.9999999999999996, 1.7320508075688774]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[μ, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E16 32.2.E16] || [[Item:Q9172|<math>\mu_{1}+\mu_{2}+\mu_{3} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu_{1}+\mu_{2}+\mu_{3} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu[1]+ mu[2]+ mu[3] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E17 32.2.E17] || [[Item:Q9173|<math>f_{1}(z)+f_{2}(z)+f_{3}(z)+2z = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{1}(z)+f_{2}(z)+f_{3}(z)+2z = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[1](z)+ f[2](z)+ f[3](z)+ 2*z = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, 1][z]+ Subscript[f, 2][z]+ Subscript[f, 3][z]+ 2*z == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E18 32.2.E18] || [[Item:Q9174|<math>(\alpha,\beta) = (\mu_{3}-\mu_{2},-2\mu_{1}^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta) = (\mu_{3}-\mu_{2},-2\mu_{1}^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta) = (mu[3]- mu[2], - 2*(mu[1])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta]) == (Subscript[\[Mu], 3]- Subscript[\[Mu], 2], - 2*(Subscript[\[Mu], 1])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.2#Ex6 32.2#Ex6] || [[Item:Q9175|<math>z\deriv{f_{1}}{z} = f_{1}f_{3}(f_{2}-f_{4})+(\tfrac{1}{2}-\mu_{3})f_{1}+\mu_{1}f_{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\deriv{f_{1}}{z} = f_{1}f_{3}(f_{2}-f_{4})+(\tfrac{1}{2}-\mu_{3})f_{1}+\mu_{1}f_{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff(f[1], z) = f[1]*f[3]*(f[2]- f[4])+((1)/(2)- mu[3])*f[1]+ mu[1]*f[3]</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[Subscript[f, 1], z] == Subscript[f, 1]*Subscript[f, 3]*(Subscript[f, 2]- Subscript[f, 4])+(Divide[1,2]- Subscript[\[Mu], 3])*Subscript[f, 1]+ Subscript[\[Mu], 1]*Subscript[f, 3]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4330127020-.2500000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.799038106-.6160254036*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.2#Ex7 32.2#Ex7] || [[Item:Q9176|<math>z\deriv{f_{2}}{z} = f_{2}f_{4}(f_{3}-f_{1})+(\tfrac{1}{2}-\mu_{4})f_{2}+\mu_{2}f_{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\deriv{f_{2}}{z} = f_{2}f_{4}(f_{3}-f_{1})+(\tfrac{1}{2}-\mu_{4})f_{2}+\mu_{2}f_{4}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff(f[2], z) = f[2]*f[4]*(f[3]- f[1])+((1)/(2)- mu[4])*f[2]+ mu[2]*f[4]</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[Subscript[f, 2], z] == Subscript[f, 2]*Subscript[f, 4]*(Subscript[f, 3]- Subscript[f, 1])+(Divide[1,2]- Subscript[\[Mu], 4])*Subscript[f, 2]+ Subscript[\[Mu], 2]*Subscript[f, 4]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4330127020-.2500000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.799038106-.6160254036*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.2#Ex8 32.2#Ex8] || [[Item:Q9177|<math>z\deriv{f_{3}}{z} = f_{3}f_{1}(f_{4}-f_{2})+(\tfrac{1}{2}-\mu_{1})f_{3}+\mu_{3}f_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\deriv{f_{3}}{z} = f_{3}f_{1}(f_{4}-f_{2})+(\tfrac{1}{2}-\mu_{1})f_{3}+\mu_{3}f_{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff(f[3], z) = f[3]*f[1]*(f[4]- f[2])+((1)/(2)- mu[1])*f[3]+ mu[3]*f[1]</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[Subscript[f, 3], z] == Subscript[f, 3]*Subscript[f, 1]*(Subscript[f, 4]- Subscript[f, 2])+(Divide[1,2]- Subscript[\[Mu], 1])*Subscript[f, 3]+ Subscript[\[Mu], 3]*Subscript[f, 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4330127020-.2500000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9330127024+.1160254036*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[1] = 1/2*3^(1/2)+1/2*I, mu[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.2#Ex9 32.2#Ex9] || [[Item:Q9178|<math>z\deriv{f_{4}}{z} = f_{4}f_{2}(f_{1}-f_{3})+(\tfrac{1}{2}-\mu_{2})f_{4}+\mu_{4}f_{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\deriv{f_{4}}{z} = f_{4}f_{2}(f_{1}-f_{3})+(\tfrac{1}{2}-\mu_{2})f_{4}+\mu_{4}f_{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*diff(f[4], z) = f[4]*f[2]*(f[1]- f[3])+((1)/(2)- mu[2])*f[4]+ mu[4]*f[2]</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*D[Subscript[f, 4], z] == Subscript[f, 4]*Subscript[f, 2]*(Subscript[f, 1]- Subscript[f, 3])+(Divide[1,2]- Subscript[\[Mu], 2])*Subscript[f, 4]+ Subscript[\[Mu], 4]*Subscript[f, 2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4330127020-.2500000000*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9330127024+.1160254036*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, f[3] = 1/2*3^(1/2)+1/2*I, f[4] = 1/2*3^(1/2)+1/2*I, mu[2] = 1/2*3^(1/2)+1/2*I, mu[4] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E20 32.2.E20] || [[Item:Q9179|<math>\mu_{1}+\mu_{2}+\mu_{3}+\mu_{4} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mu_{1}+\mu_{2}+\mu_{3}+\mu_{4} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">mu[1]+ mu[2]+ mu[3]+ mu[4] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3]+ Subscript[\[Mu], 4] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E21 32.2.E21] || [[Item:Q9180|<math>f_{1}(z)+f_{3}(z) = \sqrt{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{1}(z)+f_{3}(z) = \sqrt{z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[1](z)+ f[3](z) = sqrt(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, 1][z]+ Subscript[f, 3][z] == Sqrt[z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E22 32.2.E22] || [[Item:Q9181|<math>f_{2}(z)+f_{4}(z) = \sqrt{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>f_{2}(z)+f_{4}(z) = \sqrt{z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">f[2](z)+ f[4](z) = sqrt(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[f, 2][z]+ Subscript[f, 4][z] == Sqrt[z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E23 32.2.E23] || [[Item:Q9182|<math>(\alpha,\beta,\gamma,\delta) = (\tfrac{1}{2}\mu_{1}^{2},-\tfrac{1}{2}\mu_{3}^{2},\mu_{4}-\mu_{2},-\tfrac{1}{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = (\tfrac{1}{2}\mu_{1}^{2},-\tfrac{1}{2}\mu_{3}^{2},\mu_{4}-\mu_{2},-\tfrac{1}{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = ((1)/(2)*(mu[1])^(2), -(1)/(2)*(mu[3])^(2), mu[4]- mu[2], -(1)/(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (Divide[1,2]*(Subscript[\[Mu], 1])^(2), -Divide[1,2]*(Subscript[\[Mu], 3])^(2), Subscript[\[Mu], 4]- Subscript[\[Mu], 2], -Divide[1,2])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E25 32.2.E25] || [[Item:Q9184|<math>w(z;\alpha) = \epsilon W(\zeta)+\frac{1}{\epsilon^{5}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha) = \epsilon W(\zeta)+\frac{1}{\epsilon^{5}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha) = epsilon*W(zeta)+(1)/((epsilon)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha]] == \[Epsilon]*W[\[Zeta]]+Divide[1,\[Epsilon]^(5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex10 32.2#Ex10] || [[Item:Q9185|<math>z = \epsilon^{2}\zeta-\frac{6}{\epsilon^{10}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \epsilon^{2}\zeta-\frac{6}{\epsilon^{10}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (epsilon)^(2)* zeta -(6)/((epsilon)^(10))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == \[Epsilon]^(2)* \[Zeta]-Divide[6,\[Epsilon]^(10)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex11 32.2#Ex11] || [[Item:Q9186|<math>\alpha = \frac{4}{\epsilon^{15}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = \frac{4}{\epsilon^{15}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = (4)/((epsilon)^(15))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == Divide[4,\[Epsilon]^(15)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.2.E27 32.2.E27] || [[Item:Q9187|<math>\deriv[2]{W}{\zeta} = 6W^{2}+\zeta+\epsilon^{6}(2W^{3}+\zeta W)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{W}{\zeta} = 6W^{2}+\zeta+\epsilon^{6}(2W^{3}+\zeta W)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(W, [zeta$(2)]) = 6*(W)^(2)+ zeta + (epsilon)^(6)*(2*(W)^(3)+ zeta*W)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[W, {\[Zeta], 2}] == 6*(W)^(2)+ \[Zeta]+ \[Epsilon]^(6)*(2*(W)^(3)+ \[Zeta]*W)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.366025408-8.562177830*I
Test Values: {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -35.86602547-189.1217784*I
Test Values: {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 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[-4.366025403784439, -8.56217782649107]
Test Values: {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϵ, 1], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-35.86602540378445, -189.1217782649107]
Test Values: {Rule[W, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϵ, 2], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E28 32.2.E28] || [[Item:Q9188|<math>w(z;\alpha,\beta,\gamma,\delta) = 1+2\epsilon W(\zeta;a)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha,\beta,\gamma,\delta) = 1+2\epsilon W(\zeta;a)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha , beta , gamma , delta) = 1 + 2*epsilon*W(zeta ; a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha], \[Beta], \[Gamma], \[Delta]] == 1 + 2*\[Epsilon]*W[\[Zeta]; a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex12 32.2#Ex12] || [[Item:Q9189|<math>z = 1+\epsilon^{2}\zeta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 1+\epsilon^{2}\zeta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = 1 + (epsilon)^(2)* zeta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == 1 + \[Epsilon]^(2)* \[Zeta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex13 32.2#Ex13] || [[Item:Q9190|<math>\alpha = -\tfrac{1}{2}\epsilon^{-6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = -\tfrac{1}{2}\epsilon^{-6}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = -(1)/(2)*(epsilon)^(- 6)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == -Divide[1,2]*\[Epsilon]^(- 6)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex14 32.2#Ex14] || [[Item:Q9191|<math>\beta = \tfrac{1}{2}\epsilon^{-6}+2a\epsilon^{-3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = \tfrac{1}{2}\epsilon^{-6}+2a\epsilon^{-3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = (1)/(2)*(epsilon)^(- 6)+ 2*a*(epsilon)^(- 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == Divide[1,2]*\[Epsilon]^(- 6)+ 2*a*\[Epsilon]^(- 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex15 32.2#Ex15] || [[Item:Q9192|<math>\gamma = -\delta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma = -\delta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma = - delta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Gamma] == - \[Delta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E30 32.2.E30] || [[Item:Q9193|<math>w(z;\alpha,\beta) = 2^{2/3}\epsilon^{-1}W(\zeta;a)+\epsilon^{-3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha,\beta) = 2^{2/3}\epsilon^{-1}W(\zeta;a)+\epsilon^{-3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha , beta) = (2)^(2/3)* (epsilon)^(- 1)* W(zeta ; a)+ (epsilon)^(- 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha], \[Beta]] == (2)^(2/3)* \[Epsilon]^(- 1)* W[\[Zeta]; a]+ \[Epsilon]^(- 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex16 32.2#Ex16] || [[Item:Q9194|<math>z = 2^{-2/3}\epsilon\zeta-\epsilon^{-3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 2^{-2/3}\epsilon\zeta-\epsilon^{-3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (2)^(- 2/3)* epsilon*zeta - (epsilon)^(- 3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == (2)^(- 2/3)* \[Epsilon]*\[Zeta]- \[Epsilon]^(- 3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex17 32.2#Ex17] || [[Item:Q9195|<math>\alpha = -2a-\tfrac{1}{2}\epsilon^{-6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = -2a-\tfrac{1}{2}\epsilon^{-6}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = - 2*a -(1)/(2)*(epsilon)^(- 6)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == - 2*a -Divide[1,2]*\[Epsilon]^(- 6)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex18 32.2#Ex18] || [[Item:Q9196|<math>\beta = -\tfrac{1}{2}\epsilon^{-12}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -\tfrac{1}{2}\epsilon^{-12}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = -(1)/(2)*(epsilon)^(- 12)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == -Divide[1,2]*\[Epsilon]^(- 12)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E32 32.2.E32] || [[Item:Q9197|<math>w(z;\alpha,\beta,\gamma,\delta) = 1+\epsilon\zeta W(\zeta;a,b,c,d)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha,\beta,\gamma,\delta) = 1+\epsilon\zeta W(\zeta;a,b,c,d)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha , beta , gamma , delta) = 1 + epsilon*zeta*W(zeta ; a , b , c , d)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha], \[Beta], \[Gamma], \[Delta]] == 1 + \[Epsilon]*\[Zeta]*W[\[Zeta]; a , b , c , d]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex19 32.2#Ex19] || [[Item:Q9198|<math>z = \zeta^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \zeta^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (zeta)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == \[Zeta]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex20 32.2#Ex20] || [[Item:Q9199|<math>\alpha = \tfrac{1}{4}a\epsilon^{-1}+\tfrac{1}{8}c\epsilon^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = \tfrac{1}{4}a\epsilon^{-1}+\tfrac{1}{8}c\epsilon^{-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = (1)/(4)*a*(epsilon)^(- 1)+(1)/(8)*c*(epsilon)^(- 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == Divide[1,4]*a*\[Epsilon]^(- 1)+Divide[1,8]*c*\[Epsilon]^(- 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex21 32.2#Ex21] || [[Item:Q9200|<math>\beta = -\tfrac{1}{8}c\epsilon^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -\tfrac{1}{8}c\epsilon^{-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = -(1)/(8)*c*(epsilon)^(- 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == -Divide[1,8]*c*\[Epsilon]^(- 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex22 32.2#Ex22] || [[Item:Q9201|<math>\gamma = \tfrac{1}{4}\epsilon b</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma = \tfrac{1}{4}\epsilon b</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma = (1)/(4)*epsilon*b</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Gamma] == Divide[1,4]*\[Epsilon]*b</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex23 32.2#Ex23] || [[Item:Q9202|<math>\delta = \tfrac{1}{8}\epsilon^{2}d</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\delta = \tfrac{1}{8}\epsilon^{2}d</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">delta = (1)/(8)*(epsilon)^(2)* d</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Delta] == Divide[1,8]*\[Epsilon]^(2)* d</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E34 32.2.E34] || [[Item:Q9203|<math>w(z;\alpha,\beta,\gamma,\delta) = \tfrac{1}{2}\sqrt{2}\epsilon W(\zeta;a,b)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha,\beta,\gamma,\delta) = \tfrac{1}{2}\sqrt{2}\epsilon W(\zeta;a,b)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha , beta , gamma , delta) = (1)/(2)*sqrt(2)*epsilon*W(zeta ; a , b)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha], \[Beta], \[Gamma], \[Delta]] == Divide[1,2]*Sqrt[2]*\[Epsilon]*W[\[Zeta]; a , b]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex24 32.2#Ex24] || [[Item:Q9204|<math>z = 1+\sqrt{2}\epsilon\zeta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 1+\sqrt{2}\epsilon\zeta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = 1 +sqrt(2)*epsilon*zeta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == 1 +Sqrt[2]*\[Epsilon]*\[Zeta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex25 32.2#Ex25] || [[Item:Q9205|<math>\alpha = \tfrac{1}{2}\epsilon^{-4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = \tfrac{1}{2}\epsilon^{-4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = (1)/(2)*(epsilon)^(- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == Divide[1,2]*\[Epsilon]^(- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex26 32.2#Ex26] || [[Item:Q9206|<math>\beta = \tfrac{1}{4}b</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = \tfrac{1}{4}b</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = (1)/(4)*b</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == Divide[1,4]*b</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex27 32.2#Ex27] || [[Item:Q9207|<math>\gamma = -\epsilon^{-4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma = -\epsilon^{-4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma = - (epsilon)^(- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Gamma] == - \[Epsilon]^(- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex28 32.2#Ex28] || [[Item:Q9208|<math>\delta = a\epsilon^{-2}-\tfrac{1}{2}\epsilon^{-4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\delta = a\epsilon^{-2}-\tfrac{1}{2}\epsilon^{-4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">delta = a*(epsilon)^(- 2)-(1)/(2)*(epsilon)^(- 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Delta] == a*\[Epsilon]^(- 2)-Divide[1,2]*\[Epsilon]^(- 4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2.E36 32.2.E36] || [[Item:Q9209|<math>w(z;\alpha,\beta,\gamma,\delta) = W(\zeta;a,b,c,d)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\alpha,\beta,\gamma,\delta) = W(\zeta;a,b,c,d)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; alpha , beta , gamma , delta) = W(zeta ; a , b , c , d)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Alpha], \[Beta], \[Gamma], \[Delta]] == W[\[Zeta]; a , b , c , d]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex29 32.2#Ex29] || [[Item:Q9210|<math>z = 1+\epsilon\zeta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 1+\epsilon\zeta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = 1 + epsilon*zeta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == 1 + \[Epsilon]*\[Zeta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex30 32.2#Ex30] || [[Item:Q9211|<math>\gamma = c\epsilon^{-1}-d\epsilon^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma = c\epsilon^{-1}-d\epsilon^{-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma = c*(epsilon)^(- 1)- d*(epsilon)^(- 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Gamma] == c*\[Epsilon]^(- 1)- d*\[Epsilon]^(- 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.2#Ex31 32.2#Ex31] || [[Item:Q9212|<math>\delta = d\epsilon^{-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\delta = d\epsilon^{-2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">delta = d*(epsilon)^(- 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Delta] == d*\[Epsilon]^(- 2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.3.E2 32.3.E2] || [[Item:Q9214|<math>\deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u}{x} = 3u^{5}+2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u, [x$(2)]) = 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))*u</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[u, {x, 2}] == 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])*u</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.043949625-3.665224602*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.476962328-1.415224600*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, u = 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[3.043949623616789, -3.6652245962155616]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.67792421983235, -4.031249999999999]
Test Values: {Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.3.E4 32.3.E4] || [[Item:Q9216|<math>w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(x) = 2\sqrt{2}u_{k}^{2}(\sqrt{2}x,\nu)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(x) = 2*sqrt(2)*(u[k])^(2)(sqrt(2)*x , nu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[x] == 2*Sqrt[2]*(Subscript[u, k])^(2)[Sqrt[2]*x , \[Nu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.3.E6 32.3.E6] || [[Item:Q9218|<math>u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u^{2} = -\tfrac{1}{3}x+\tfrac{1}{6}\sqrt{x^{2}+12\nu+6}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(u)^(2) = -(1)/(3)*x +(1)/(6)*sqrt((x)^(2)+ 12*nu + 6)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(u)^(2) == -Divide[1,3]*x +Divide[1,6]*Sqrt[(x)^(2)+ 12*\[Nu]+ 6]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.4#Ex1 32.4#Ex1] || [[Item:Q9219|<math>\pderiv{\boldsymbol{{\Psi}}}{\lambda} = \mathbf{A}(z,\lambda)\boldsymbol{{\Psi}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{\boldsymbol{{\Psi}}}{\lambda} = \mathbf{A}(z,\lambda)\boldsymbol{{\Psi}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(Psi, lambda) = A(z , lambda)* Psi</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[\[CapitalPsi], \[Lambda]] == A[z , \[Lambda]]* \[CapitalPsi]</syntaxhighlight> || Failure || Failure || Error || Error
|-
| [https://dlmf.nist.gov/32.4#Ex2 32.4#Ex2] || [[Item:Q9220|<math>\pderiv{\boldsymbol{{\Psi}}}{z} = \mathbf{B}(z,\lambda)\boldsymbol{{\Psi}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{\boldsymbol{{\Psi}}}{z} = \mathbf{B}(z,\lambda)\boldsymbol{{\Psi}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(Psi, z) = B(z , lambda)* Psi</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[\[CapitalPsi], z] == B[z , \[Lambda]]* \[CapitalPsi]</syntaxhighlight> || Failure || Failure || Error || Error
|-
| [https://dlmf.nist.gov/32.4.E3 32.4.E3] || [[Item:Q9222|<math>\pderiv{\mathbf{A}}{z}-\pderiv{\mathbf{B}}{\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv{\mathbf{A}}{z}-\pderiv{\mathbf{B}}{\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(A, z)- diff(B, lambda)+ A*B - B*A = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[A, z]- D[B, \[Lambda]]+ A*B - B*A == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.4.E15 32.4.E15] || [[Item:Q9234|<math>(\alpha,\beta,\gamma,\delta) = \left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = \left(2\theta_{0},2(1-\theta_{\infty}),1,-1\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = (2*theta[0], 2*(1 - theta[infinity]), 1 , - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (2*Subscript[\[Theta], 0], 2*(1 - Subscript[\[Theta], Infinity]), 1 , - 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.4.E16 32.4.E16] || [[Item:Q9235|<math>\theta_{0} = \frac{4v_{0}}{z}\left(\theta_{\infty}\left(1-\frac{z}{4v_{0}}\right)+\frac{z-2v_{0}}{2v_{0}v_{1}}u_{0}+u_{1}v_{1}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\theta_{0} = \frac{4v_{0}}{z}\left(\theta_{\infty}\left(1-\frac{z}{4v_{0}}\right)+\frac{z-2v_{0}}{2v_{0}v_{1}}u_{0}+u_{1}v_{1}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">theta[0] = (4*v[0])/(z)*(theta[infinity]*(1 -(z)/(4*v[0]))+(z - 2*v[0])/(2*v[0]*v[1])*u[0]+ u[1]*v[1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Theta], 0] == Divide[4*Subscript[v, 0],z]*(Subscript[\[Theta], Infinity]*(1 -Divide[z,4*Subscript[v, 0]])+Divide[z - 2*Subscript[v, 0],2*Subscript[v, 0]*Subscript[v, 1]]*Subscript[u, 0]+ Subscript[u, 1]*Subscript[v, 1])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.5.E1 32.5.E1] || [[Item:Q9236|<math>K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>K(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>K[z , \[Zeta]] == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K[z , s]* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Error
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.5.E2 32.5.E2] || [[Item:Q9237|<math>w(z) = K(z,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = K(z,z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = K(z , z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == K[z , z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.6#Ex1 32.6#Ex1] || [[Item:Q9239|<math>\deriv{q}{z} = \pderiv{\mathrm{H}}{p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{q}{z} = \pderiv{\mathrm{H}}{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(q, z) = diff(H, p)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[q, z] == D[H, p]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/32.6#Ex2 32.6#Ex2] || [[Item:Q9240|<math>\deriv{p}{z} = -\pderiv{\mathrm{H}}{q}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{p}{z} = -\pderiv{\mathrm{H}}{q}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(p, z) = - diff(H, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[p, z] == - D[H, q]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.6.E19 32.6.E19] || [[Item:Q9258|<math>(\alpha,\beta,\gamma,\delta) = \left(-2\kappa_{\infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{0}^{2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = \left(-2\kappa_{\infty}\theta_{\infty},2\kappa_{0}(\theta_{0}+1),\kappa_{\infty}^{2},-\kappa_{0}^{2}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = (- 2*kappa[infinity]*theta[infinity], 2*kappa[0]*(theta[0]+ 1), (kappa[infinity])^(2), - (kappa[0])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (- 2*Subscript[\[Kappa], Infinity]*Subscript[\[Theta], Infinity], 2*Subscript[\[Kappa], 0]*(Subscript[\[Theta], 0]+ 1), (Subscript[\[Kappa], Infinity])^(2), - (Subscript[\[Kappa], 0])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.6.E27 32.6.E27] || [[Item:Q9266|<math>(\alpha,\beta,\gamma,\delta) = \left(-4\eta_{\infty}\theta_{\infty},4\eta_{0}(\theta_{0}+1),4\eta_{\infty}^{2},-4\eta_{0}^{2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = \left(-4\eta_{\infty}\theta_{\infty},4\eta_{0}(\theta_{0}+1),4\eta_{\infty}^{2},-4\eta_{0}^{2}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = (- 4*eta[infinity]*theta[infinity], 4*eta[0]*(theta[0]+ 1), 4*(eta[infinity])^(2), - 4*(eta[0])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (- 4*Subscript[\[Eta], Infinity]*Subscript[\[Theta], Infinity], 4*Subscript[\[Eta], 0]*(Subscript[\[Theta], 0]+ 1), 4*(Subscript[\[Eta], Infinity])^(2), - 4*(Subscript[\[Eta], 0])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.6.E35 32.6.E35] || [[Item:Q9274|<math>(\alpha,\beta,\gamma,\delta) = \left(2\kappa_{\infty},\kappa_{0}(\theta-1),0,-\kappa_{0}^{2}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = \left(2\kappa_{\infty},\kappa_{0}(\theta-1),0,-\kappa_{0}^{2}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = (2*kappa[infinity], kappa[0]*(theta - 1), 0 , - (kappa[0])^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (2*Subscript[\[Kappa], Infinity], Subscript[\[Kappa], 0]*(\[Theta]- 1), 0 , - (Subscript[\[Kappa], 0])^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.7.E3 32.7.E3] || [[Item:Q9281|<math>W(\zeta;\tfrac{1}{2}\varepsilon) = \frac{2^{-1/3}\varepsilon}{w(z;0)}\deriv{}{z}w(z;0)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>W(\zeta;\tfrac{1}{2}\varepsilon) = \frac{2^{-1/3}\varepsilon}{w(z;0)}\deriv{}{z}w(z;0)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>W(zeta ;(1)/(2)*varepsilon) = ((2)^(- 1/3)* varepsilon)/(w(z ; 0))*diff(w(z ; 0), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]] == Divide[(2)^(- 1/3)* \[CurlyEpsilon],w[z ; 0]]*D[w[z ; 0], z]</syntaxhighlight> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/32.7.E4 32.7.E4] || [[Item:Q9282|<math>w^{2}(z;0) = 2^{-1/3}\left(W^{2}(\zeta;\tfrac{1}{2}\varepsilon)-\varepsilon\deriv{}{\zeta}W(\zeta;\tfrac{1}{2}\varepsilon)+\tfrac{1}{2}\zeta\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w^{2}(z;0) = 2^{-1/3}\left(W^{2}(\zeta;\tfrac{1}{2}\varepsilon)-\varepsilon\deriv{}{\zeta}W(\zeta;\tfrac{1}{2}\varepsilon)+\tfrac{1}{2}\zeta\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(w(z ; 0))^(2) = (2)^(- 1/3)*((W(zeta ;(1)/(2)*varepsilon))^(2)- varepsilon*diff(W(zeta ;(1)/(2)*varepsilon)+(1)/(2)*zeta, zeta))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(w[z ; 0])^(2) == (2)^(- 1/3)*((W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]])^(2)- \[CurlyEpsilon]*D[W[\[Zeta];Divide[1,2]*\[CurlyEpsilon]]+Divide[1,2]*\[Zeta], \[Zeta]])</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E5 32.7.E5] || [[Item:Q9283|<math>\frac{\alpha+\tfrac{1}{2}}{w_{\alpha+1}+w_{\alpha}}+\frac{\alpha-\tfrac{1}{2}}{w_{\alpha}+w_{\alpha-1}}+2w_{\alpha}^{2}+z = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{\alpha+\tfrac{1}{2}}{w_{\alpha+1}+w_{\alpha}}+\frac{\alpha-\tfrac{1}{2}}{w_{\alpha}+w_{\alpha-1}}+2w_{\alpha}^{2}+z = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha +(1)/(2))/(w[alpha + 1]+ w[alpha])+(alpha -(1)/(2))/(w[alpha]+ w[alpha - 1])+ 2*(w[alpha])^(2)+ z = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[\[Alpha]+Divide[1,2],Subscript[w, \[Alpha]+ 1]+ Subscript[w, \[Alpha]]]+Divide[\[Alpha]-Divide[1,2],Subscript[w, \[Alpha]]+ Subscript[w, \[Alpha]- 1]]+ 2*(Subscript[w, \[Alpha]])^(2)+ z == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E6 32.7.E6] || [[Item:Q9284|<math>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (-\alpha_{0},-\beta_{0},\gamma_{0},\delta_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (-\alpha_{0},-\beta_{0},\gamma_{0},\delta_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[1], beta[1], gamma[1], delta[1]) = (- alpha[0], - beta[0], gamma[0], delta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (- Subscript[\[Alpha], 0], - Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E7 32.7.E7] || [[Item:Q9285|<math>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\delta_{0},-\gamma_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\delta_{0},-\gamma_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - delta[0], - gamma[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Delta], 0], - Subscript[\[Gamma], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex1 32.7#Ex1] || [[Item:Q9288|<math>\alpha_{1} = \alpha_{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{1} = \alpha_{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[1] = alpha[3]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 1] == Subscript[\[Alpha], 3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex2 32.7#Ex2] || [[Item:Q9289|<math>\alpha_{2} = \alpha_{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2} = \alpha_{4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2] = alpha[4]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2] == Subscript[\[Alpha], 4]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex3 32.7#Ex3] || [[Item:Q9290|<math>\beta_{1} = \beta_{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{1} = \beta_{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[1] = beta[2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], 1] == Subscript[\[Beta], 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex4 32.7#Ex4] || [[Item:Q9291|<math>\beta_{3} = \beta_{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{3} = \beta_{4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[3] = beta[4]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], 3] == Subscript[\[Beta], 4]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex5 32.7#Ex5] || [[Item:Q9296|<math>\beta_{5} = \beta_{0}+2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{5} = \beta_{0}+2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[5] = beta[0]+ 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], 5] == Subscript[\[Beta], 0]+ 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex6 32.7#Ex6] || [[Item:Q9297|<math>\beta_{6} = \beta_{0}-2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{6} = \beta_{0}-2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[6] = beta[0]- 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], 6] == Subscript[\[Beta], 0]- 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex7 32.7#Ex7] || [[Item:Q9300|<math>w(z;a,b,0,0) = W^{2}(\zeta;0,0,a,b)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;a,b,0,0) = W^{2}(\zeta;0,0,a,b)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; a , b , 0 , 0) = (W(zeta ; 0 , 0 , a , b))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; a , b , 0 , 0] == (W[\[Zeta]; 0 , 0 , a , b])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex8 32.7#Ex8] || [[Item:Q9301|<math>z = \tfrac{1}{2}\zeta^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \tfrac{1}{2}\zeta^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = (1)/(2)*(zeta)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == Divide[1,2]*\[Zeta]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex9 32.7#Ex9] || [[Item:Q9302|<math>\alpha_{1}^{+} = \tfrac{1}{4}\left(2-2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{1}^{+} = \tfrac{1}{4}\left(2-2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[1])^(+) = (1)/(4)*(2 - 2*alpha[0]+ 3*sqrt(- 2*beta[0]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 1])^(+) == Divide[1,4]*(2 - 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex10 32.7#Ex10] || [[Item:Q9303|<math>\beta_{1}^{+} = -\tfrac{1}{2}\left(1+\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{1}^{+} = -\tfrac{1}{2}\left(1+\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(beta[1])^(+) = -(1)/(2)*(1 + alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Beta], 1])^(+) == -Divide[1,2]*(1 + Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex11 32.7#Ex11] || [[Item:Q9304|<math>\alpha_{2}^{+} = -\tfrac{1}{4}\left(2+2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2}^{+} = -\tfrac{1}{4}\left(2+2\alpha_{0}+ 3\sqrt{-2\beta_{0}}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[2])^(+) = -(1)/(4)*(2 + 2*alpha[0]+ 3*sqrt(- 2*beta[0]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 2])^(+) == -Divide[1,4]*(2 + 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex12 32.7#Ex12] || [[Item:Q9305|<math>\beta_{2}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{2}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(beta[2])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Beta], 2])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex13 32.7#Ex13] || [[Item:Q9306|<math>\alpha_{3}^{+} = \tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{3}^{+} = \tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[3])^(+) = (3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 3])^(+) == Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex14 32.7#Ex14] || [[Item:Q9307|<math>\beta_{3}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{3}^{+} = -\tfrac{1}{2}\left(1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(beta[3])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Beta], 3])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex15 32.7#Ex15] || [[Item:Q9308|<math>\alpha_{4}^{+} = -\tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{4}^{+} = -\tfrac{3}{2}-\tfrac{1}{2}\alpha_{0}-\tfrac{3}{4}\sqrt{-2\beta_{0}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[4])^(+) = -(3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 4])^(+) == -Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex16 32.7#Ex16] || [[Item:Q9309|<math>\beta_{4}^{+} = -\tfrac{1}{2}\left(-1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{4}^{+} = -\tfrac{1}{2}\left(-1-\alpha_{0}+\tfrac{1}{2}\sqrt{-2\beta_{0}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(beta[4])^(+) = -(1)/(2)*(- 1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Beta], 4])^(+) == -Divide[1,2]*(- 1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex17 32.7#Ex17] || [[Item:Q9314|<math>z_{1} = -z_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{1} = -z_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[1] = - z[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, 1] == - Subscript[z, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex18 32.7#Ex18] || [[Item:Q9315|<math>z_{2} = z_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{2} = z_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[2] = z[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, 2] == Subscript[z, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex19 32.7#Ex19] || [[Item:Q9316|<math>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\gamma_{0},\delta_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\gamma_{0},\delta_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - gamma[0], delta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex20 32.7#Ex20] || [[Item:Q9317|<math>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\gamma_{0},\delta_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (-\beta_{0},-\alpha_{0},-\gamma_{0},\delta_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - gamma[0], delta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex21 32.7#Ex21] || [[Item:Q9320|<math>\alpha_{1} = \tfrac{1}{8}\left(\gamma_{0}+\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{1} = \tfrac{1}{8}\left(\gamma_{0}+\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[1] = (1)/(8)*(gamma[0]+ varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 1] == Divide[1,8]*(Subscript[\[Gamma], 0]+ Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex22 32.7#Ex22] || [[Item:Q9321|<math>\beta_{1} = -\tfrac{1}{8}\left(\gamma_{0}-\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{1} = -\tfrac{1}{8}\left(\gamma_{0}-\varepsilon_{1}\left(1-\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[1] = -(1)/(8)*(gamma[0]- varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], 1] == -Divide[1,8]*(Subscript[\[Gamma], 0]- Subscript[\[CurlyEpsilon], 1]*(1 - Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]]))^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex23 32.7#Ex23] || [[Item:Q9322|<math>\gamma_{1} = \varepsilon_{1}\left(\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{1} = \varepsilon_{1}\left(\varepsilon_{3}\sqrt{-2\beta_{0}}-\varepsilon_{2}\sqrt{2\alpha_{0}}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">gamma[1] = varepsilon[1]*(varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Gamma], 1] == Subscript[\[CurlyEpsilon], 1]*(Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex24 32.7#Ex24] || [[Item:Q9326|<math>W(\zeta;\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = \frac{v-1}{v+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>W(\zeta;\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = \frac{v-1}{v+1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W(zeta ; alpha[0], beta[0], gamma[0], delta[0]) = (v - 1)/(v + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">W[\[Zeta]; Subscript[\[Alpha], 0], Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]] == Divide[v - 1,v + 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex25 32.7#Ex25] || [[Item:Q9327|<math>z = \sqrt{2\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \sqrt{2\zeta}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = sqrt(2*zeta)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == Sqrt[2*\[Zeta]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E32 32.7.E32] || [[Item:Q9328|<math>(\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = {\left((\beta-\varepsilon\alpha+2)^{2}/32,-(\beta+\varepsilon\alpha-2)^{2}/32,-\varepsilon,0\right)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{0},\beta_{0},\gamma_{0},\delta_{0}) = {\left((\beta-\varepsilon\alpha+2)^{2}/32,-(\beta+\varepsilon\alpha-2)^{2}/32,-\varepsilon,0\right)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[0], beta[0], gamma[0], delta[0]) = ((beta - varepsilon*alpha + 2)^(2)/32 , -(beta + varepsilon*alpha - 2)^(2)/32 , - varepsilon , 0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 0], Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0]) == ((\[Beta]- \[CurlyEpsilon]*\[Alpha]+ 2)^(2)/32 , -(\[Beta]+ \[CurlyEpsilon]*\[Alpha]- 2)^(2)/32 , - \[CurlyEpsilon], 0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E33 32.7.E33] || [[Item:Q9329|<math>z_{1} = 1/z_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{1} = 1/z_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[1] = 1/z[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, 1] == 1/Subscript[z, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E34 32.7.E34] || [[Item:Q9330|<math>z_{2} = 1-z_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{2} = 1-z_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[2] = 1 - z[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, 2] == 1 - Subscript[z, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E35 32.7.E35] || [[Item:Q9331|<math>z_{3} = 1/z_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{3} = 1/z_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[3] = 1/z[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, 3] == 1/Subscript[z, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E36 32.7.E36] || [[Item:Q9332|<math>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\delta_{0}+\tfrac{1}{2},-\gamma_{0}+\tfrac{1}{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{1},\beta_{1},\gamma_{1},\delta_{1}) = (\alpha_{0},\beta_{0},-\delta_{0}+\tfrac{1}{2},-\gamma_{0}+\tfrac{1}{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - delta[0]+(1)/(2), - gamma[0]+(1)/(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Delta], 0]+Divide[1,2], - Subscript[\[Gamma], 0]+Divide[1,2])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E37 32.7.E37] || [[Item:Q9333|<math>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (\alpha_{0},-\gamma_{0},-\beta_{0},\delta_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{2},\beta_{2},\gamma_{2},\delta_{2}) = (\alpha_{0},-\gamma_{0},-\beta_{0},\delta_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[2], beta[2], gamma[2], delta[2]) = (alpha[0], - gamma[0], - beta[0], delta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], - Subscript[\[Beta], 0], Subscript[\[Delta], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E38 32.7.E38] || [[Item:Q9334|<math>(\alpha_{3},\beta_{3},\gamma_{3},\delta_{3}) = (-\beta_{0},-\alpha_{0},\gamma_{0},\delta_{0})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha_{3},\beta_{3},\gamma_{3},\delta_{3}) = (-\beta_{0},-\alpha_{0},\gamma_{0},\delta_{0})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha[3], beta[3], gamma[3], delta[3]) = (- beta[0], - alpha[0], gamma[0], delta[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[\[Alpha], 3], Subscript[\[Beta], 3], Subscript[\[Gamma], 3], Subscript[\[Delta], 3]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E42 32.7.E42] || [[Item:Q9338|<math>(\alpha,\beta,\gamma,\delta) = \left(\tfrac{1}{2}(\theta_{\infty}-1)^{2},-\tfrac{1}{2}\theta_{0}^{2},\tfrac{1}{2}\theta_{1}^{2},\tfrac{1}{2}(1-\theta_{2}^{2})\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(\alpha,\beta,\gamma,\delta) = \left(\tfrac{1}{2}(\theta_{\infty}-1)^{2},-\tfrac{1}{2}\theta_{0}^{2},\tfrac{1}{2}\theta_{1}^{2},\tfrac{1}{2}(1-\theta_{2}^{2})\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma , delta) = ((1)/(2)*(theta[infinity]- 1)^(2), -(1)/(2)*(theta[0])^(2),(1)/(2)*(theta[1])^(2),(1)/(2)*(1 - (theta[2])^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (Divide[1,2]*(Subscript[\[Theta], Infinity]- 1)^(2), -Divide[1,2]*(Subscript[\[Theta], 0])^(2),Divide[1,2]*(Subscript[\[Theta], 1])^(2),Divide[1,2]*(1 - (Subscript[\[Theta], 2])^(2)))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E43 32.7.E43] || [[Item:Q9339|<math>(A,B,C,D) = \left(\tfrac{1}{2}(\Theta_{\infty}-1)^{2},-\tfrac{1}{2}\Theta_{0}^{2},\tfrac{1}{2}\Theta_{1}^{2},\tfrac{1}{2}(1-\Theta_{2}^{2})\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(A,B,C,D) = \left(\tfrac{1}{2}(\Theta_{\infty}-1)^{2},-\tfrac{1}{2}\Theta_{0}^{2},\tfrac{1}{2}\Theta_{1}^{2},\tfrac{1}{2}(1-\Theta_{2}^{2})\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A , B , C , D) = ((1)/(2)*(Theta[infinity]- 1)^(2), -(1)/(2)*(Theta[0])^(2),(1)/(2)*(Theta[1])^(2),(1)/(2)*(1 - (Theta[2])^(2)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(A , B , C , D) == (Divide[1,2]*(Subscript[\[CapitalTheta], Infinity]- 1)^(2), -Divide[1,2]*(Subscript[\[CapitalTheta], 0])^(2),Divide[1,2]*(Subscript[\[CapitalTheta], 1])^(2),Divide[1,2]*(1 - (Subscript[\[CapitalTheta], 2])^(2)))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E44 32.7.E44] || [[Item:Q9340|<math>\theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">theta[j] = Theta[j]+(1)/(2)*sigma</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Theta], j] == Subscript[\[CapitalTheta], j]+Divide[1,2]*\[Sigma]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E45 32.7.E45] || [[Item:Q9341|<math>\sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sigma = theta[0]+ theta[1]+ theta[2]+ theta[infinity]- 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Sigma] == Subscript[\[Theta], 0]+ Subscript[\[Theta], 1]+ Subscript[\[Theta], 2]+ Subscript[\[Theta], Infinity]- 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex26 32.7#Ex26] || [[Item:Q9343|<math>u_{1}(\zeta_{1}) = \frac{(1-w)(w-z)}{(1+\sqrt{z})^{2}w}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{1}(\zeta_{1}) = \frac{(1-w)(w-z)}{(1+\sqrt{z})^{2}w}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[1](zeta[1]) = ((1 - w)*(w - z))/((1 +sqrt(z))^(2)* w)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, 1][Subscript[\[Zeta], 1]] == Divide[(1 - w)*(w - z),(1 +Sqrt[z])^(2)* w]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex27 32.7#Ex27] || [[Item:Q9344|<math>\zeta_{1} = \left(\frac{1-\sqrt{z}}{1+\sqrt{z}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta_{1} = \left(\frac{1-\sqrt{z}}{1+\sqrt{z}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta[1] = ((1 -sqrt(z))/(1 +sqrt(z)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Zeta], 1] == (Divide[1 -Sqrt[z],1 +Sqrt[z]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex28 32.7#Ex28] || [[Item:Q9345|<math>u_{2}(\zeta_{2}) = \frac{(w^{2}-z)^{2}}{4w(w-1)(w-z)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{2}(\zeta_{2}) = \frac{(w^{2}-z)^{2}}{4w(w-1)(w-z)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[2](zeta[2]) = (((w)^(2)- z)^(2))/(4*w*(w - 1)*(w - z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, 2][Subscript[\[Zeta], 2]] == Divide[((w)^(2)- z)^(2),4*w*(w - 1)*(w - z)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7#Ex29 32.7#Ex29] || [[Item:Q9346|<math>\zeta_{2} = z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta_{2} = z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta[2] = z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Zeta], 2] == z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E49 32.7.E49] || [[Item:Q9347|<math>u_{3}(\zeta_{3}) = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{2}\left(\frac{\sqrt{w}+z^{1/4}}{\sqrt{w}-z^{1/4}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{3}(\zeta_{3}) = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{2}\left(\frac{\sqrt{w}+z^{1/4}}{\sqrt{w}-z^{1/4}}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[3](zeta[3]) = ((1 - (z)^(1/4))/(1 + (z)^(1/4)))^(2)*((sqrt(w)+ (z)^(1/4))/(sqrt(w)- (z)^(1/4)))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, 3][Subscript[\[Zeta], 3]] == (Divide[1 - (z)^(1/4),1 + (z)^(1/4)])^(2)*(Divide[Sqrt[w]+ (z)^(1/4),Sqrt[w]- (z)^(1/4)])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.7.E50 32.7.E50] || [[Item:Q9348|<math>\zeta_{3} = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta_{3} = \left(\frac{1-z^{1/4}}{1+z^{1/4}}\right)^{4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta[3] = ((1 - (z)^(1/4))/(1 + (z)^(1/4)))^(4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Zeta], 3] == (Divide[1 - (z)^(1/4),1 + (z)^(1/4)])^(4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E1 32.8.E1] || [[Item:Q9349|<math>w(z;1) = -\ifrac{1}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;1) = -\ifrac{1}{z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 1) = -(1)/(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 1] == -Divide[1,z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E2 32.8.E2] || [[Item:Q9350|<math>w(z;2) = \frac{1}{z}-\frac{3z^{2}}{z^{3}+4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;2) = \frac{1}{z}-\frac{3z^{2}}{z^{3}+4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 2) = (1)/(z)-(3*(z)^(2))/((z)^(3)+ 4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 2] == Divide[1,z]-Divide[3*(z)^(2),(z)^(3)+ 4]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E3 32.8.E3] || [[Item:Q9351|<math>w(z;3) = \frac{3z^{2}}{z^{3}+4}-\frac{6z^{2}(z^{3}+10)}{z^{6}+20z^{3}-80}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;3) = \frac{3z^{2}}{z^{3}+4}-\frac{6z^{2}(z^{3}+10)}{z^{6}+20z^{3}-80}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 3) = (3*(z)^(2))/((z)^(3)+ 4)-(6*(z)^(2)*((z)^(3)+ 10))/((z)^(6)+ 20*(z)^(3)- 80)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 3] == Divide[3*(z)^(2),(z)^(3)+ 4]-Divide[6*(z)^(2)*((z)^(3)+ 10),(z)^(6)+ 20*(z)^(3)- 80]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E4 32.8.E4] || [[Item:Q9352|<math>w(z;4) = -\frac{1}{z}+\frac{6z^{2}(z^{3}+10)}{z^{6}+20z^{3}-80}-\frac{9z^{5}(z^{3}+40)}{z^{9}+60z^{6}+11200}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;4) = -\frac{1}{z}+\frac{6z^{2}(z^{3}+10)}{z^{6}+20z^{3}-80}-\frac{9z^{5}(z^{3}+40)}{z^{9}+60z^{6}+11200}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 4) = -(1)/(z)+(6*(z)^(2)*((z)^(3)+ 10))/((z)^(6)+ 20*(z)^(3)- 80)-(9*(z)^(5)*((z)^(3)+ 40))/((z)^(9)+ 60*(z)^(6)+ 11200)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 4] == -Divide[1,z]+Divide[6*(z)^(2)*((z)^(3)+ 10),(z)^(6)+ 20*(z)^(3)- 80]-Divide[9*(z)^(5)*((z)^(3)+ 40),(z)^(9)+ 60*(z)^(6)+ 11200]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.8.E5 32.8.E5] || [[Item:Q9353|<math>w(z;n) = \deriv{}{z}\left(\ln@{\frac{Q_{n-1}(z)}{Q_{n}(z)}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;n) = \deriv{}{z}\left(\ln@{\frac{Q_{n-1}(z)}{Q_{n}(z)}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; n) = diff(ln((Q[n - 1](z))/(Q[n](z))), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; n] == D[Log[Divide[Subscript[Q, n - 1][z],Subscript[Q, n][z]]], z]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex1 32.8#Ex1] || [[Item:Q9355|<math>Q_{2}(z) = z^{3}+4</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{2}(z) = z^{3}+4</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[2](z) = (z)^(3)+ 4</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 2][z] == (z)^(3)+ 4</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex2 32.8#Ex2] || [[Item:Q9356|<math>Q_{3}(z) = z^{6}+20z^{3}-80</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{3}(z) = z^{6}+20z^{3}-80</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[3](z) = (z)^(6)+ 20*(z)^(3)- 80</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 3][z] == (z)^(6)+ 20*(z)^(3)- 80</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex3 32.8#Ex3] || [[Item:Q9357|<math>Q_{4}(z) = z^{10}+60z^{7}+11200z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{4}(z) = z^{10}+60z^{7}+11200z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[4](z) = (z)^(10)+ 60*(z)^(7)+ 11200*z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 4][z] == (z)^(10)+ 60*(z)^(7)+ 11200*z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex4 32.8#Ex4] || [[Item:Q9358|<math>Q_{5}(z) = z^{15}+140z^{12}+2800z^{9}+78400z^{6}-3\;13600z^{3}-62\;72000</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{5}(z) = z^{15}+140z^{12}+2800z^{9}+78400z^{6}-3\;13600z^{3}-62\;72000</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[5](z) = (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 5][z] == (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex5 32.8#Ex5] || [[Item:Q9359|<math>Q_{6}(z) = z^{21}+280z^{18}+18480z^{15}+6\;27200z^{12}-172\;48000z^{9}+14488\;32000z^{6}+1\;93177\;60000z^{3}-3\;86355\;20000</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Q_{6}(z) = z^{21}+280z^{18}+18480z^{15}+6\;27200z^{12}-172\;48000z^{9}+14488\;32000z^{6}+1\;93177\;60000z^{3}-3\;86355\;20000</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Q[6](z) = (z)^(21)+ 280*(z)^(18)+ 18480*(z)^(15)+ 627200*(z)^(12)- 17248000*(z)^(9)+ 1448832000*(z)^(6)+ 19317760000*(z)^(3)- 38635520000</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Q, 6][z] == (z)^(21)+ 280*(z)^(18)+ 18480*(z)^(15)+ 627200*(z)^(12)- 17248000*(z)^(9)+ 1448832000*(z)^(6)+ 19317760000*(z)^(3)- 38635520000</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.8.E8 32.8.E8] || [[Item:Q9360|<math>\sum_{m=0}^{\infty}p_{m}(z)\lambda^{m} = \exp@{z\lambda-\tfrac{4}{3}\lambda^{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{m=0}^{\infty}p_{m}(z)\lambda^{m} = \exp@{z\lambda-\tfrac{4}{3}\lambda^{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(p[m](z)* (lambda)^(m), m = 0..infinity) = exp(z*lambda -(4)/(3)*(lambda)^(3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Subscript[p, m][z]* \[Lambda]^(m), {m, 0, Infinity}, GenerateConditions->None] == Exp[z*\[Lambda]-Divide[4,3]*\[Lambda]^(3)]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.4719523959894307, 0.7427233484952657], NSum[Times[Power[E, Times[Complex[0, Rational[1, 3]], Pi]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], m]]
Test Values: {m, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.4719523959894307, 0.7427233484952657], NSum[Times[Power[E, Times[Complex[0, Rational[5, 6]], Pi]], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], m]]
Test Values: {m, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.8.E9 32.8.E9] || [[Item:Q9361|<math>w(z;n) = \deriv{}{z}\left(\ln@{\frac{\tau_{n-1}(z)}{\tau_{n}(z)}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;n) = \deriv{}{z}\left(\ln@{\frac{\tau_{n-1}(z)}{\tau_{n}(z)}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; n) = diff(ln((tau[n - 1](z))/(tau[n](z))), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; n] == D[Log[Divide[Subscript[\[Tau], n - 1][z],Subscript[\[Tau], n][z]]], z]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E11 32.8.E11] || [[Item:Q9363|<math>w(z;\mu,-\mu\kappa^{2},\lambda,-\lambda\kappa^{4}) = \kappa</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\mu,-\mu\kappa^{2},\lambda,-\lambda\kappa^{4}) = \kappa</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; mu , - mu*(kappa)^(2), lambda , - lambda*(kappa)^(4)) = kappa</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Mu], - \[Mu]*\[Kappa]^(2), \[Lambda], - \[Lambda]*\[Kappa]^(4)] == \[Kappa]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E12 32.8.E12] || [[Item:Q9364|<math>w(z;0,-\mu,0,\mu\kappa) = \kappa z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;0,-\mu,0,\mu\kappa) = \kappa z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 0 , - mu , 0 , mu*kappa) = kappa*z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 0 , - \[Mu], 0 , \[Mu]*\[Kappa]] == \[Kappa]*z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E13 32.8.E13] || [[Item:Q9365|<math>w(z;2\kappa+3,-2\kappa+1,1,-1) = \dfrac{z+\kappa}{z+\kappa+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;2\kappa+3,-2\kappa+1,1,-1) = \dfrac{z+\kappa}{z+\kappa+1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 2*kappa + 3 , - 2*kappa + 1 , 1 , - 1) = (z + kappa)/(z + kappa + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 2*\[Kappa]+ 3 , - 2*\[Kappa]+ 1 , 1 , - 1] == Divide[z + \[Kappa],z + \[Kappa]+ 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E14 32.8.E14] || [[Item:Q9366|<math>\alpha+\beta = 4n</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha+\beta = 4n</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha + beta = 4*n</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha]+ \[Beta] == 4*n</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E15 32.8.E15] || [[Item:Q9367|<math>w(z) = \ifrac{P_{m}(z)}{Q_{m}(z)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = \ifrac{P_{m}(z)}{Q_{m}(z)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = (P[m](z))/(Q[m](z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Divide[Subscript[P, m][z],Subscript[Q, m][z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E16 32.8.E16] || [[Item:Q9368|<math>w_{1}(z;+ 2,-2) = +\ifrac{1}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{1}(z;+ 2,-2) = +\ifrac{1}{z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[1](z ; + 2 , - 2) = +(1)/(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 1][z ; + 2 , - 2] == +Divide[1,z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E17 32.8.E17] || [[Item:Q9369|<math>w_{2}(z;0,-2) = -2z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{2}(z;0,-2) = -2z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[2](z ; 0 , - 2) = - 2*z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 2][z ; 0 , - 2] == - 2*z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E18 32.8.E18] || [[Item:Q9370|<math>w_{3}(z;0,-\tfrac{2}{9}) = -\tfrac{2}{3}z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{3}(z;0,-\tfrac{2}{9}) = -\tfrac{2}{3}z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[3](z ; 0 , -(2)/(9)) = -(2)/(3)*z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 3][z ; 0 , -Divide[2,9]] == -Divide[2,3]*z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E19 32.8.E19] || [[Item:Q9371|<math>w_{1}(z;\alpha_{1},\beta_{1}) = \ifrac{P_{1,n-1}(z)}{Q_{1,n}(z)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{1}(z;\alpha_{1},\beta_{1}) = \ifrac{P_{1,n-1}(z)}{Q_{1,n}(z)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[1](z ; alpha[1], beta[1]) = (P[1 , n - 1](z))/(Q[1 , n](z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 1][z ; Subscript[\[Alpha], 1], Subscript[\[Beta], 1]] == Divide[Subscript[P, 1 , n - 1][z],Subscript[Q, 1 , n][z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E20 32.8.E20] || [[Item:Q9372|<math>w_{2}(z;\alpha_{2},\beta_{2}) = -2z+(\ifrac{P_{2,n-1}(z)}{Q_{2,n}(z)})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{2}(z;\alpha_{2},\beta_{2}) = -2z+(\ifrac{P_{2,n-1}(z)}{Q_{2,n}(z)})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[2](z ; alpha[2], beta[2]) = - 2*z +((P[2 , n - 1](z))/(Q[2 , n](z)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 2][z ; Subscript[\[Alpha], 2], Subscript[\[Beta], 2]] == - 2*z +(Divide[Subscript[P, 2 , n - 1][z],Subscript[Q, 2 , n][z]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E21 32.8.E21] || [[Item:Q9373|<math>w_{3}(z;\alpha_{3},\beta_{3}) = -\tfrac{2}{3}z+(\ifrac{P_{3,n-1}(z)}{Q_{3,n}(z)})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{3}(z;\alpha_{3},\beta_{3}) = -\tfrac{2}{3}z+(\ifrac{P_{3,n-1}(z)}{Q_{3,n}(z)})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[3](z ; alpha[3], beta[3]) = -(2)/(3)*z +((P[3 , n - 1](z))/(Q[3 , n](z)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 3][z ; Subscript[\[Alpha], 3], Subscript[\[Beta], 3]] == -Divide[2,3]*z +(Divide[Subscript[P, 3 , n - 1][z],Subscript[Q, 3 , n][z]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex6 32.8#Ex6] || [[Item:Q9374|<math>\alpha = m</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = m</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = m</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == m</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex7 32.8#Ex7] || [[Item:Q9375|<math>\beta = -2(1+2n-m)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -2(1+2n-m)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = - 2*(1 + 2*n - m)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == - 2*(1 + 2*n - m)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex8 32.8#Ex8] || [[Item:Q9376|<math>\mspace{12.0mu }\alpha = m</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mspace{12.0mu }\alpha = m</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = m</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == m</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8#Ex9 32.8#Ex9] || [[Item:Q9377|<math>\beta = -2(\tfrac{1}{3}+2n-m)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -2(\tfrac{1}{3}+2n-m)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = - 2*((1)/(3)+ 2*n - m)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == - 2*(Divide[1,3]+ 2*n - m)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E24 32.8.E24] || [[Item:Q9378|<math>w(z;\tfrac{1}{2},-\tfrac{1}{2}\mu^{2},\kappa(2-\mu),-\tfrac{1}{2}\kappa^{2}) = \kappa z+\mu</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{1}{2},-\tfrac{1}{2}\mu^{2},\kappa(2-\mu),-\tfrac{1}{2}\kappa^{2}) = \kappa z+\mu</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(1)/(2), -(1)/(2)*(mu)^(2), kappa*(2 - mu), -(1)/(2)*(kappa)^(2)) = kappa*z + mu</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[1,2], -Divide[1,2]*\[Mu]^(2), \[Kappa]*(2 - \[Mu]), -Divide[1,2]*\[Kappa]^(2)] == \[Kappa]*z + \[Mu]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E25 32.8.E25] || [[Item:Q9379|<math>w(z;\tfrac{1}{2},\kappa^{2}\mu,2\kappa\mu,\mu) = \kappa/(z+\kappa)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{1}{2},\kappa^{2}\mu,2\kappa\mu,\mu) = \kappa/(z+\kappa)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(1)/(2), (kappa)^(2)* mu , 2*kappa*mu , mu) = kappa/(z + kappa)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[1,2], \[Kappa]^(2)* \[Mu], 2*\[Kappa]*\[Mu], \[Mu]] == \[Kappa]/(z + \[Kappa])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E26 32.8.E26] || [[Item:Q9380|<math>w(z;\tfrac{1}{8},-\tfrac{1}{8},-\kappa\mu,\mu) = (\kappa+z)/(\kappa-z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{1}{8},-\tfrac{1}{8},-\kappa\mu,\mu) = (\kappa+z)/(\kappa-z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(1)/(8), -(1)/(8), - kappa*mu , mu) = (kappa + z)/(kappa - z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[1,8], -Divide[1,8], - \[Kappa]*\[Mu], \[Mu]] == (\[Kappa]+ z)/(\[Kappa]- z)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E27 32.8.E27] || [[Item:Q9381|<math>w(z) = \lambda z+\mu+(\ifrac{P_{n-1}(z)}{Q_{n}(z)})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = \lambda z+\mu+(\ifrac{P_{n-1}(z)}{Q_{n}(z)})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = lambda*z + mu +((P[n - 1](z))/(Q[n](z)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == \[Lambda]*z + \[Mu]+(Divide[Subscript[P, n - 1][z],Subscript[Q, n][z]])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E28 32.8.E28] || [[Item:Q9382|<math>w(z;\mu,-\mu\kappa^{2},\tfrac{1}{2},\tfrac{1}{2}-\mu(\kappa-1)^{2}) = \kappa z</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\mu,-\mu\kappa^{2},\tfrac{1}{2},\tfrac{1}{2}-\mu(\kappa-1)^{2}) = \kappa z</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; mu , - mu*(kappa)^(2),(1)/(2),(1)/(2)- mu*(kappa - 1)^(2)) = kappa*z</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Mu], - \[Mu]*\[Kappa]^(2),Divide[1,2],Divide[1,2]- \[Mu]*(\[Kappa]- 1)^(2)] == \[Kappa]*z</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E29 32.8.E29] || [[Item:Q9383|<math>w(z;0,0,2,0) = \kappa z^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;0,0,2,0) = \kappa z^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 0 , 0 , 2 , 0) = kappa*(z)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 0 , 0 , 2 , 0] == \[Kappa]*(z)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E30 32.8.E30] || [[Item:Q9384|<math>w(z;0,0,\tfrac{1}{2},-\tfrac{3}{2}) = \ifrac{\kappa}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;0,0,\tfrac{1}{2},-\tfrac{3}{2}) = \ifrac{\kappa}{z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 0 , 0 ,(1)/(2), -(3)/(2)) = (kappa)/(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 0 , 0 ,Divide[1,2], -Divide[3,2]] == Divide[\[Kappa],z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E31 32.8.E31] || [[Item:Q9385|<math>w(z;0,0,2,-4) = \ifrac{\kappa}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;0,0,2,-4) = \ifrac{\kappa}{z^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 0 , 0 , 2 , - 4) = (kappa)/((z)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 0 , 0 , 2 , - 4] == Divide[\[Kappa],(z)^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E32 32.8.E32] || [[Item:Q9386|<math>w(z;\tfrac{1}{2}(\kappa+\mu)^{2},-\tfrac{1}{2},\tfrac{1}{2}(\mu-1)^{2},\tfrac{1}{2}\kappa(2-\kappa)) = \dfrac{z}{\kappa+\mu z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{1}{2}(\kappa+\mu)^{2},-\tfrac{1}{2},\tfrac{1}{2}(\mu-1)^{2},\tfrac{1}{2}\kappa(2-\kappa)) = \dfrac{z}{\kappa+\mu z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(1)/(2)*(kappa + mu)^(2), -(1)/(2),(1)/(2)*(mu - 1)^(2),(1)/(2)*kappa*(2 - kappa)) = (z)/(kappa + mu*z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[1,2]*(\[Kappa]+ \[Mu])^(2), -Divide[1,2],Divide[1,2]*(\[Mu]- 1)^(2),Divide[1,2]*\[Kappa]*(2 - \[Kappa])] == Divide[z,\[Kappa]+ \[Mu]*z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.8.E33 32.8.E33] || [[Item:Q9387|<math>a+b+c+d = 2n+1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a+b+c+d = 2n+1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + c + d = 2*n + 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + c + d == 2*n + 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E1 32.9.E1] || [[Item:Q9388|<math>w(z;\mu,0,0,-\mu\kappa^{3}) = \kappa z^{1/3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\mu,0,0,-\mu\kappa^{3}) = \kappa z^{1/3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; mu , 0 , 0 , - mu*(kappa)^(3)) = kappa*(z)^(1/3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Mu], 0 , 0 , - \[Mu]*\[Kappa]^(3)] == \[Kappa]*(z)^(1/3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.9.E2 32.9.E2] || [[Item:Q9389|<math>w(z;0,-2\kappa,0,4\kappa\mu-\lambda^{2}) = z(\kappa(\ln@@{z})^{2}+\lambda\ln@@{z}+\mu)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;0,-2\kappa,0,4\kappa\mu-\lambda^{2}) = z(\kappa(\ln@@{z})^{2}+\lambda\ln@@{z}+\mu)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; 0 , - 2*kappa(,)*0 , 4*kappa(mu)- (lambda)^(2)) = z*((kappa(ln(z)))^(2)+ lambda*ln(z)+ mu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; 0 , - 2*\[Kappa][,]*0 , 4*\[Kappa][Mu]- \[Lambda]^(2)] == z*((\[Kappa][Log[z]])^(2)+ \[Lambda]*Log[z]+ \[Mu])</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E3 32.9.E3] || [[Item:Q9390|<math>w(z;-\nu^{2}\lambda,0,\nu^{2}(\lambda^{2}-4\kappa\mu),0) = \dfrac{z^{\nu-1}}{\kappa z^{2\nu}+\lambda z^{\nu}+\mu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;-\nu^{2}\lambda,0,\nu^{2}(\lambda^{2}-4\kappa\mu),0) = \dfrac{z^{\nu-1}}{\kappa z^{2\nu}+\lambda z^{\nu}+\mu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; - (nu)^(2)* lambda , 0 , (nu)^(2)*((lambda)^(2)- 4*kappa*mu), 0) = ((z)^(nu - 1))/(kappa*(z)^(2*nu)+ lambda*(z)^(nu)+ mu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; - \[Nu]^(2)* \[Lambda], 0 , \[Nu]^(2)*(\[Lambda]^(2)- 4*\[Kappa]*\[Mu]), 0] == Divide[(z)^(\[Nu]- 1),\[Kappa]*(z)^(2*\[Nu])+ \[Lambda]*(z)^\[Nu]+ \[Mu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E4 32.9.E4] || [[Item:Q9391|<math>\beta = 2n</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = 2n</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = 2*n</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == 2*n</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E5 32.9.E5] || [[Item:Q9392|<math>w(z) = \ifrac{P_{n^{2}+1}(\zeta)}{Q_{n^{2}}(\zeta)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = \ifrac{P_{n^{2}+1}(\zeta)}{Q_{n^{2}}(\zeta)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = (P[(n)^(2)+ 1](zeta))/(Q[(n)^(2)](zeta))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Divide[Subscript[P, (n)^(2)+ 1][\[Zeta]],Subscript[Q, (n)^(2)][\[Zeta]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E7 32.9.E7] || [[Item:Q9394|<math>w(z;\mu,-\tfrac{1}{8},-\mu\kappa^{2},0) = 1+\kappa z^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\mu,-\tfrac{1}{8},-\mu\kappa^{2},0) = 1+\kappa z^{1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; mu , -(1)/(8), - mu*(kappa)^(2), 0) = 1 + kappa*(z)^(1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; \[Mu], -Divide[1,8], - \[Mu]*\[Kappa]^(2), 0] == 1 + \[Kappa]*(z)^(1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.9.E8 32.9.E8] || [[Item:Q9395|<math>w(z;0,0,\mu,-\tfrac{1}{2}\mu^{2}) = \kappa\exp@{\mu z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;0,0,\mu,-\tfrac{1}{2}\mu^{2}) = \kappa\exp@{\mu z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; 0 , 0 , mu , -(1)/(2)*(mu)^(2)) = kappa*exp(mu*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; 0 , 0 , \[Mu], -Divide[1,2]*\[Mu]^(2)] == \[Kappa]*Exp[\[Mu]*z]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E9 32.9.E9] || [[Item:Q9396|<math>\mspace{17.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{2}\mu^{2},-\tfrac{1}{8}(2n-1)^{2},-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mspace{17.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{2}\mu^{2},-\tfrac{1}{8}(2n-1)^{2},-1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma) = ((1)/(2)*(mu)^(2), -(1)/(8)*(2*n - 1)^(2), - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,2]*\[Mu]^(2), -Divide[1,8]*(2*n - 1)^(2), - 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E10 32.9.E10] || [[Item:Q9397|<math>\mspace{5.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{8}(2n-1)^{2},-\tfrac{1}{2}\mu^{2},1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mspace{5.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{8}(2n-1)^{2},-\tfrac{1}{2}\mu^{2},1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(alpha , beta , gamma) = ((1)/(8)*(2*n - 1)^(2), -(1)/(2)*(mu)^(2), 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,8]*(2*n - 1)^(2), -Divide[1,2]*\[Mu]^(2), 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E11 32.9.E11] || [[Item:Q9398|<math>w(z) = \ifrac{P_{n^{2}-n+1}(\zeta)}{Q_{n^{2}-n}(\zeta)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = \ifrac{P_{n^{2}-n+1}(\zeta)}{Q_{n^{2}-n}(\zeta)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = (P[(n)^(2)- n + 1](zeta))/(Q[(n)^(2)- n](zeta))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == Divide[Subscript[P, (n)^(2)- n + 1][\[Zeta]],Subscript[Q, (n)^(2)- n][\[Zeta]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.9.E13 32.9.E13] || [[Item:Q9400|<math>w(z;\tfrac{1}{2}\kappa^{2},-\tfrac{1}{2}\kappa^{2},\tfrac{1}{2}\mu^{2},\tfrac{1}{2}(1-\mu^{2})) = z^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{1}{2}\kappa^{2},-\tfrac{1}{2}\kappa^{2},\tfrac{1}{2}\mu^{2},\tfrac{1}{2}(1-\mu^{2})) = z^{1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(1)/(2)*(kappa)^(2), -(1)/(2)*(kappa)^(2),(1)/(2)*(mu)^(2),(1)/(2)*(1 - (mu)^(2))) = (z)^(1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[1,2]*\[Kappa]^(2), -Divide[1,2]*\[Kappa]^(2),Divide[1,2]*\[Mu]^(2),Divide[1,2]*(1 - \[Mu]^(2))] == (z)^(1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E2 32.10.E2] || [[Item:Q9402|<math>\alpha = n+\tfrac{1}{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha = n+\tfrac{1}{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha = n +(1)/(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Alpha] == n +Divide[1,2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E5 32.10.E5] || [[Item:Q9405|<math>\phi(z) = C_{1}\AiryAi@{-2^{-1/3}z}+C_{2}\AiryBi@{-2^{-1/3}z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(z) = C_{1}\AiryAi@{-2^{-1/3}z}+C_{2}\AiryBi@{-2^{-1/3}z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(z) = C[1]*AiryAi(- (2)^(- 1/3)* z)+ C[2]*AiryBi(- (2)^(- 1/3)* z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][z] == Subscript[C, 1]*AiryAi[- (2)^(- 1/3)* z]+ Subscript[C, 2]*AiryBi[- (2)^(- 1/3)* z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2986692739+.5787509238*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3018910357e-1+.1740730853*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.29866927421000106, 0.5787509234724151]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.03018910341830547, 0.174073084997731]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E6 32.10.E6] || [[Item:Q9406|<math>w(z;\tfrac{3}{2}) = \Phi-\dfrac{1}{2\Phi^{2}+z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{3}{2}) = \Phi-\dfrac{1}{2\Phi^{2}+z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(3)/(2)) = Phi -(1)/(2*(Phi)^(2)+ z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[3,2]] == \[CapitalPhi]-Divide[1,2*\[CapitalPhi]^(2)+ z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E7 32.10.E7] || [[Item:Q9407|<math>w(z;\tfrac{5}{2}) = \dfrac{1}{2\Phi^{2}+z}+\dfrac{2z\Phi^{2}+\Phi+z^{2}}{4\Phi^{3}+2z\Phi-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;\tfrac{5}{2}) = \dfrac{1}{2\Phi^{2}+z}+\dfrac{2z\Phi^{2}+\Phi+z^{2}}{4\Phi^{3}+2z\Phi-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ;(5)/(2)) = (1)/(2*(Phi)^(2)+ z)+(2*z*(Phi)^(2)+ Phi + (z)^(2))/(4*(Phi)^(3)+ 2*z*Phi - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ;Divide[5,2]] == Divide[1,2*\[CapitalPhi]^(2)+ z]+Divide[2*z*\[CapitalPhi]^(2)+ \[CapitalPhi]+ (z)^(2),4*\[CapitalPhi]^(3)+ 2*z*\[CapitalPhi]- 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E8 32.10.E8] || [[Item:Q9408|<math>w(z;n+\tfrac{1}{2}) = \deriv{}{z}\left(\ln@{\frac{\tau_{n}(z)}{\tau_{n+1}(z)}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;n+\tfrac{1}{2}) = \deriv{}{z}\left(\ln@{\frac{\tau_{n}(z)}{\tau_{n+1}(z)}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; n +(1)/(2)) = diff(ln((tau[n](z))/(tau[n + 1](z))), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; n +Divide[1,2]] == D[Log[Divide[Subscript[\[Tau], n][z],Subscript[\[Tau], n + 1][z]]], z]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E10 32.10.E10] || [[Item:Q9410|<math>w(z;-n-\tfrac{1}{2}) = -w(z;n+\tfrac{1}{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;-n-\tfrac{1}{2}) = -w(z;n+\tfrac{1}{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; - n -(1)/(2)) = - w(z ; n +(1)/(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; - n -Divide[1,2]] == - w[z ; n +Divide[1,2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E11 32.10.E11] || [[Item:Q9411|<math>\varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">varepsilon[1]*alpha + varepsilon[2]*beta = 4*n + 2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[CurlyEpsilon], 1]*\[Alpha]+ Subscript[\[CurlyEpsilon], 2]*\[Beta] == 4*n + 2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E14 32.10.E14] || [[Item:Q9414|<math>\phi(z) = z^{\nu}\left(C_{1}\BesselJ{\nu}@{\zeta}+C_{2}\BesselY{\nu}@{\zeta}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(z) = z^{\nu}\left(C_{1}\BesselJ{\nu}@{\zeta}+C_{2}\BesselY{\nu}@{\zeta}\right)</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>phi(z) = (z)^(nu)*(C[1]*BesselJ(nu, zeta)+ C[2]*BesselY(nu, zeta))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][z] == (z)^\[Nu]*(Subscript[C, 1]*BesselJ[\[Nu], \[Zeta]]+ Subscript[C, 2]*BesselY[\[Nu], \[Zeta]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6857713611+1.049278090*I
Test Values: {nu = 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, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1639325500+1.038275666*I
Test Values: {nu = 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, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6857713606630202, 1.0492780901981935]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.16393255022963316, 1.0382756660889538]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E15 32.10.E15] || [[Item:Q9415|<math>\beta = -2(2n+1+\varepsilon\alpha)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -2(2n+1+\varepsilon\alpha)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = - 2*(2*n + 1 + varepsilon*alpha)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == - 2*(2*n + 1 + \[CurlyEpsilon]*\[Alpha])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E16 32.10.E16] || [[Item:Q9416|<math>\beta = -2n^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta = -2n^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta = - 2*(n)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Beta] == - 2*(n)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E19 32.10.E19] || [[Item:Q9419|<math>\phi(z) = \left(C_{1}\paraU@{a}{\sqrt{2}z}+C_{2}\paraV@{a}{\sqrt{2}z}\right)\exp@{\tfrac{1}{2}\varepsilon z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(z) = \left(C_{1}\paraU@{a}{\sqrt{2}z}+C_{2}\paraV@{a}{\sqrt{2}z}\right)\exp@{\tfrac{1}{2}\varepsilon z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(z) = (C[1]*CylinderU(a, sqrt(2)*z)+ C[2]*CylinderV(a, sqrt(2)*z))*exp((1)/(2)*varepsilon*(z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][z] == (Subscript[C, 1]*ParabolicCylinderD[- 1/2 -(a), Sqrt[2]*z]+ Subscript[C, 2]*Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, Sqrt[2]*z] + ParabolicCylinderD[-(a) - 1/2, -(Sqrt[2]*z)]))*Exp[Divide[1,2]*\[CurlyEpsilon]*(z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6213533818-.8057984780*I
Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.542195596-1.017130546*I
Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 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: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.165517214154348, -0.5387865015105858], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]]
Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.0681394822800956, -1.2559298845291706], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]]
Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/32.10.E20 32.10.E20] || [[Item:Q9420|<math>w(z;-m,-2(m-1)^{2}) = -\frac{\HermitepolyH{m-1}'@{z}}{\HermitepolyH{m-1}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;-m,-2(m-1)^{2}) = -\frac{\HermitepolyH{m-1}'@{z}}{\HermitepolyH{m-1}@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; - m , - 2*(m - 1)^(2)) = -(diff( HermiteH(m - 1, z), z$(1) ))/(HermiteH(m - 1, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; - m , - 2*(m - 1)^(2)] == -Divide[D[HermiteH[m - 1, z], {z, 1}],HermiteH[m - 1, z]]</syntaxhighlight> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/32.10.E21 32.10.E21] || [[Item:Q9421|<math>w(z;-m,-2(m+1)^{2}) = -2z+\frac{\HermitepolyH{m}'@{z}}{\HermitepolyH{m}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z;-m,-2(m+1)^{2}) = -2z+\frac{\HermitepolyH{m}'@{z}}{\HermitepolyH{m}@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z ; - m , - 2*(m + 1)^(2)) = - 2*z +(diff( HermiteH(m, z), z$(1) ))/(HermiteH(m, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z ; - m , - 2*(m + 1)^(2)] == - 2*z +Divide[D[HermiteH[m, z], {z, 1}],HermiteH[m, z]]</syntaxhighlight> || Translation Error || Translation Error || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E23 32.10.E23] || [[Item:Q9423|<math>a+b+\varepsilon_{3}\gamma = 2n+1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a+b+\varepsilon_{3}\gamma = 2n+1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + varepsilon[3]*gamma = 2*n + 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + Subscript[\[CurlyEpsilon], 3]*\[Gamma] == 2*n + 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E24 32.10.E24] || [[Item:Q9424|<math>(a-n)(b-n) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(a-n)(b-n) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - n)*(b - n) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(a - n)*(b - n) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E27 32.10.E27] || [[Item:Q9427|<math>\phi(z) = \frac{C_{1}\WhittakerconfhyperM{\kappa}{\mu}@{\zeta}+C_{2}\WhittakerconfhyperW{\kappa}{\mu}@{\zeta}}{\zeta^{(a-b+1)/2}}\exp@{\tfrac{1}{2}\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(z) = \frac{C_{1}\WhittakerconfhyperM{\kappa}{\mu}@{\zeta}+C_{2}\WhittakerconfhyperW{\kappa}{\mu}@{\zeta}}{\zeta^{(a-b+1)/2}}\exp@{\tfrac{1}{2}\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(z) = (C[1]*WhittakerM(kappa, mu, zeta)+ C[2]*WhittakerW(kappa, mu, zeta))/((zeta)^((a - b + 1)/2))*exp((1)/(2)*zeta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][z] == Divide[Subscript[C, 1]*WhittakerM[\[Kappa], \[Mu], \[Zeta]]+ Subscript[C, 2]*WhittakerW[\[Kappa], \[Mu], \[Zeta]],\[Zeta]^((a - b + 1)/2)]*Exp[Divide[1,2]*\[Zeta]]</syntaxhighlight> || Failure || Failure || Manual Skip! || Skipped - Because timed out
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E28 32.10.E28] || [[Item:Q9428|<math>a+b+c+d = 2n+1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a+b+c+d = 2n+1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + c + d = 2*n + 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a + b + c + d == 2*n + 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10#Ex2 32.10#Ex2] || [[Item:Q9431|<math>\zeta = \frac{1}{1-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\zeta = \frac{1}{1-z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">zeta = (1)/(1 - z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Zeta] == Divide[1,1 - z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.10.E31 32.10.E31] || [[Item:Q9432|<math>\phi(\zeta) = C_{1}\hyperF@{b}{-a}{b+c}{\zeta}+C_{2}\zeta^{-b+1-c}\*\hyperF@{-a-b-c+1}{-c+1}{2-b-c}{\zeta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(\zeta) = C_{1}\hyperF@{b}{-a}{b+c}{\zeta}+C_{2}\zeta^{-b+1-c}\*\hyperF@{-a-b-c+1}{-c+1}{2-b-c}{\zeta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(zeta) = C[1]*hypergeom([b, - a], [b + c], zeta)+ C[2]*(zeta)^(- b + 1 - c)* hypergeom([- a - b - c + 1, - c + 1], [2 - b - c], zeta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][\[Zeta]] == Subscript[C, 1]*Hypergeometric2F1[b, - a, b + c, \[Zeta]]+ Subscript[C, 2]*\[Zeta]^(- b + 1 - c)* Hypergeometric2F1[- a - b - c + 1, - c + 1, 2 - b - c, \[Zeta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.10.E32 32.10.E32] || [[Item:Q9433|<math>u = \int_{0}^{\Lambda}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>u = \int_{0}^{\Lambda}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>u = int((1)/(sqrt(t*(t - 1)*(t - z))), t = 0..Lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>u == Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, 0, \[CapitalLambda]}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/32.10.E33 32.10.E33] || [[Item:Q9434|<math>z(1-z)\deriv[2]{\phi}{z}+(1-2z)\deriv{\phi}{z}-\tfrac{1}{4}\phi = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z(1-z)\deriv[2]{\phi}{z}+(1-2z)\deriv{\phi}{z}-\tfrac{1}{4}\phi = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*(1 - z)*diff(phi, [z$(2)])+(1 - 2*z)*diff(phi, z)-(1)/(4)*phi = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*(1 - z)*D[\[Phi], {z, 2}]+(1 - 2*z)*D[\[Phi], z]-Divide[1,4]*\[Phi] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2165063510-.1250000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2165063510-.1250000000*I
Test Values: {phi = 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 [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.21650635094610968, -0.12499999999999999]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.12499999999999994, -0.21650635094610968]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.10.E34 32.10.E34] || [[Item:Q9435|<math>w(z;0,0,0,\tfrac{1}{2}) = \Lambda(C_{1}\phi_{1}+C_{2}\phi_{2},z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z;0,0,0,\tfrac{1}{2}) = \Lambda(C_{1}\phi_{1}+C_{2}\phi_{2},z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z ; 0 , 0 , 0 ,(1)/(2)) = Lambda(C[1]*phi[1]+ C[2]*phi[2], z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z ; 0 , 0 , 0 ,Divide[1,2]] == \[CapitalLambda][Subscript[C, 1]*Subscript[\[Phi], 1]+ Subscript[C, 2]*Subscript[\[Phi], 2], z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.11.E2 32.11.E2] || [[Item:Q9437|<math>\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] || [[Item:Q9442|<math>\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] || [[Item:Q9443|<math>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] || [[Item:Q9444|<math>\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] || [[Item:Q9449|<math>\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] || [[Item:Q9450|<math>\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] || [[Item:Q9452|<math>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] || [[Item:Q9453|<math>\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] || [[Item:Q9455|<math>\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] || [[Item:Q9456|<math>\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] || [[Item:Q9457|<math>\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] || [[Item:Q9458|<math>\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] || [[Item:Q9462|<math>\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] || [[Item:Q9463|<math>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] || [[Item:Q9466|<math>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] || [[Item:Q9469|<math>\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] || [[Item:Q9470|<math>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] || [[Item:Q9471|<math>\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] || [[Item:Q9472|<math>\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>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13.E1 32.13.E1] || [[Item:Q9474|<math>v_{t}-6v^{2}v_{x}+v_{xxx} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>v_{t}-6v^{2}v_{x}+v_{xxx} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v[t]- 6*(v)^(2)* v[x]+ v[x, x, x] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[v, t]- 6*(v)^(2)* Subscript[v, x]+ Subscript[v, x, x, x] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex1 32.13#Ex1] || [[Item:Q9475|<math>z = x(3t)^{-1/3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = x(3t)^{-1/3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x(+)*y*I) = (x(3*t))^(- 1/3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x[+]*y*I) == (x[3*t])^(- 1/3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex2 32.13#Ex2] || [[Item:Q9476|<math>v(x,t) = (3t)^{-1/3}w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>v(x,t) = (3t)^{-1/3}w(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v(x , t) = (3*t)^(- 1/3)* w*((x + y*I))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">v[x , t] == (3*t)^(- 1/3)* w*((x + y*I))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13.E3 32.13.E3] || [[Item:Q9477|<math>u_{t}+6uu_{x}+u_{xxx} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{t}+6uu_{x}+u_{xxx} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[t]+ 6*u*u[x]+ u[x, x, x] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x, x, x] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex3 32.13#Ex3] || [[Item:Q9478|<math>z = x(3t)^{-1/3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = x(3t)^{-1/3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x(+)*y*I) = (x(3*t))^(- 1/3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x[+]*y*I) == (x[3*t])^(- 1/3)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex5 32.13#Ex5] || [[Item:Q9480|<math>z = x+3\lambda t^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = x+3\lambda t^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) = x + 3*lambda*(t)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) == x + 3*\[Lambda]*(t)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex6 32.13#Ex6] || [[Item:Q9481|<math>u(x,t) = W(z)-\lambda t</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u(x,t) = W(z)-\lambda t</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u(x , t) = W*((x + y*I))- lambda*t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[x , t] == W*((x + y*I))- \[Lambda]*t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.13.E6 32.13.E6] || [[Item:Q9482|<math>u_{xt} = \sin@@{u}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>u_{xt} = \sin@@{u}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>u[x, t] = sin(u)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[u, x, t] == Sin[u]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .70450695e-2+.1624035369*I
Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.358980334+.5284289409*I
Test Values: {t = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, u[x*t] = -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[0.007045069484300837, 0.16240353677712993]
Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.3589803343001376, 0.5284289405615687]
Test Values: {Rule[t, -1.5], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[u, Times[t, x]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex7 32.13#Ex7] || [[Item:Q9483|<math>z = xt</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = xt</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) = x*t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) == x*t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex8 32.13#Ex8] || [[Item:Q9484|<math>u(x,t) = v(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u(x,t) = v(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u(x , t) = v*((x + y*I))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[x , t] == v*((x + y*I))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13.E8 32.13.E8] || [[Item:Q9485|<math>u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[t, t] = u[x, x]- 6*(u)^(2)[x, x]+ u[x, x, x, x]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, t, t] == Subscript[u, x, x]- 6*Subscript[(u)^(2), x, x]+ Subscript[u, x, x, x, x]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex9 32.13#Ex9] || [[Item:Q9486|<math>z = x-ct</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = x-ct</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) = x - c*t</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(x + y*I) == x - c*t</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.13#Ex10 32.13#Ex10] || [[Item:Q9487|<math>u(x,t) = v(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u(x,t) = v(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u(x , t) = v*((x + y*I))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[x , t] == v*((x + y*I))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/32.15.E1 32.15.E1] || [[Item:Q9493|<math>\int_{-\infty}^{\infty}\exp@{-\tfrac{1}{4}\xi^{4}-z\xi^{2}}p_{m}(\xi)p_{n}(\xi)\diff{\xi} = \Kroneckerdelta{m}{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{-\infty}^{\infty}\exp@{-\tfrac{1}{4}\xi^{4}-z\xi^{2}}p_{m}(\xi)p_{n}(\xi)\diff{\xi} = \Kroneckerdelta{m}{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(exp(-(1)/(4)*(xi)^(4)- z*(xi)^(2))*p[m](xi)* p[n](xi), xi = - infinity..infinity) = KroneckerDelta[m, n]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[-Divide[1,4]*\[Xi]^(4)- z*\[Xi]^(2)]*Subscript[p, m][\[Xi]]* Subscript[p, n][\[Xi]], {\[Xi], - Infinity, Infinity}, GenerateConditions->None] == KroneckerDelta[m, n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5089051774+.3195154069*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, p[m] = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4910948226+.3195154069*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, p[m] = 1/2*3^(1/2)+1/2*I, p[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5089051767265081, 0.31951540648426185]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.49109482327349185, 0.31951540648426185]
Test Values: {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[p, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.15.E2 32.15.E2] || [[Item:Q9494|<math>a_{n+1}(z)p_{n+1}(\xi) = \xi p_{n}(\xi)-a_{n}(z)p_{n-1}(\xi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n+1}(z)p_{n+1}(\xi) = \xi p_{n}(\xi)-a_{n}(z)p_{n-1}(\xi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n + 1](z)* p[n + 1](xi) = xi*p[n](xi)- a[n](z)* p[n - 1](xi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n + 1][z]* Subscript[p, n + 1][\[Xi]] == \[Xi]*Subscript[p, n][\[Xi]]- Subscript[a, n][z]* Subscript[p, n - 1][\[Xi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/32.15.E3 32.15.E3] || [[Item:Q9495|<math>(u_{n+1}+u_{n}+u_{n-1})u_{n} = n-2zu_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>(u_{n+1}+u_{n}+u_{n-1})u_{n} = n-2zu_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(u[n + 1]+ u[n]+ u[n - 1])*u[n] = n - 2*z*u[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[u, n + 1]+ Subscript[u, n]+ Subscript[u, n - 1])*Subscript[u, n] == n - 2*z*Subscript[u, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
</div>
</div>

Latest revision as of 17:55, 25 May 2021

Notation
32.1 Special Notation
Properties
32.2 Differential Equations
32.3 Graphics
32.4 Isomonodromy Problems
32.5 Integral Equations
32.6 Hamiltonian Structure
32.7 Bäcklund Transformations
32.8 Rational Solutions
32.9 Other Elementary Solutions
32.10 Special Function Solutions
32.11 Asymptotic Approximations for Real Variables
32.12 Asymptotic Approximations for Complex Variables
Applications
32.13 Reductions of Partial Differential Equations
32.14 Combinatorics
32.15 Orthogonal Polynomials
32.16 Physical Applications
Computation
32.17 Methods of Computation
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