Results of Painlevé Transcendents: Difference between revisions

VisualWikitext

Latest revision as of 18:55, 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

@@ Line 1: / Line 1: @@
-{| class="wikitable sortable"
+<div style="-moz-column-count:2; column-count:2;">
-|-
+; Notation : [[32.1|32.1 Special Notation]]<br>
-! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
+; 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>
-|-
+; 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>
-| [https://dlmf.nist.gov/32.2.E1 32.2.E1] || [[Item:Q9154|<math>\deriv[2]{w}{z} = 6w^{2}+z</math>]] || <code>diff(w, [z$(2)]) = 6*(w)^(2)+ z</code> || <code>D[w, {z, 2}] == 6*(w)^(2)+ z</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>70/70]: [[-3.866025406-5.696152424*I <- {w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-2.500000002-6.062177828*I <- {w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[-3.8660254037844397, -5.696152422706632] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.500000000000001, -6.06217782649107] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
+; Computation : [[32.17|32.17 Methods of Computation]]<br>
-|-
+</div>
-| [https://dlmf.nist.gov/32.2.E2 32.2.E2] || [[Item:Q9155|<math>\deriv[2]{w}{z} = 2w^{3}+zw+\alpha</math>]] || <code>diff(w, [z$(2)]) = 2*(w)^(3)+ z*w + alpha</code> || <code>D[w, {z, 2}] == 2*(w)^(3)+ z*w + \[Alpha]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [209 / 210]<div class="mw-collapsible-content"><code>209/210]: [[-2.000000001-2.866025406*I <- {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.6339745966-2.500000002*I <- {alpha = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [209 / 210]<div class="mw-collapsible-content"><code>{Complex[-2.0, -2.8660254037844384] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</code><br><code>Complex[-1.0, -2.8660254037844384] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-3.598076212-.5772156656*I <- {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}</code><br><code>-1.000000000+2.020860546*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><code>{Complex[-3.098076211353316, -0.8660254037844389] <- {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]]]}</code><br><code>Complex[-2.098076211353316, -1.8660254037844388] <- {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]]]}</code><br></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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><code>299/300]: [[1.299038104-5.250000007*I <- {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>5.299038110+2.749999997*I <- {alpha = 3/2, beta = 3/2, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.2990381056766576, -5.25] <- {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]}</code><br><code>Complex[2.1650635094610964, -5.75] <- {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]}</code><br></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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-3.206380793+1.517949194*I <- {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}</code><br><code>-3.834936494+2.791317281*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-3.495190528383291, 1.017949192431124] <- {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]]]}</code><br><code>Complex[-2.1291651245988517, -4.0801270189221945] <- {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]]]}</code><br></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>]] || <code>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)))</code> || <code>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)])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [269 / 300]<div class="mw-collapsible-content"><code>269/300]: [[-.9380246356e-1+1.316803425*I <- {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)}</code><br><code>1.739453154+1.182694224*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {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]]]}</code><br><code>Indeterminate <- {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]]]}</code><br></div></div>
-|-
-| [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>]] || <code>W*(zeta) = (a*(z)* w + b*(z))/(c*(z)* w + d*(z))</code> || <code>W*(\[Zeta]) == Divide[a*(z)* w + b*(z),c*(z)* w + d*(z)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex2 32.2#Ex2] || [[Item:Q9162|<math>\zeta = \phi(z)</math>]] || <code>zeta = phi*(z)</code> || <code>\[Zeta] == \[Phi]*(z)</code> || 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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-1.074730384+.1153480418*I <- {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}</code><br><code>.4374708571+.3969114845*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.0747595264191645, -0.029006350946109677] <- {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]]]}</code><br><code>Complex[0.4374999999999999, 0.541265877365274] <- {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]]]}</code><br></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>]] || <code>diff(u, [z$(2)])+(1)/(z)*diff(u, z) = (2*alpha)/(z)*sin(u)+ 2*gamma*sin(2*u)</code> || <code>D[u, {z, 2}]+Divide[1,z]*D[u, z] == Divide[2*\[Alpha],z]*Sin[u]+ 2*\[Gamma]*Sin[2*u]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-4.496361213+.6291944644*I <- {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}</code><br><code>-1.346900984+2.955916370*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-5.5647975539874, -0.7848783935570325] <- {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]]]}</code><br><code>Complex[-1.5418435125289267, -2.4153373252737342] <- {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]]]}</code><br></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>]] || <code>diff(u, [zeta$(2)]) = 3*(u)^(5)+ 2*zeta*(u)^(3)+((1)/(4)*(zeta)^(2)- nu -(1)/(2))* u +(beta)/(32*(u)^(3))</code> || <code>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)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[4.531088915-2.319150408*I <- {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}</code><br><code>5.263139725+.9129004010*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[4.531088913245536, -2.3191504037844384] <- {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]]]}</code><br><code>Complex[3.165063509461097, -2.685175807568877] <- {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]]]}</code><br></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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-10.15437375-4.132059394*I <- {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}</code><br><code>-.1182986371-1.333346640*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-10.983749451492802, -3.604532198424999] <- {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]]]}</code><br><code>Complex[-0.3640397236276506, -1.2834088930332135] <- {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]]]}</code><br></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>]] || <code>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)))</code> || <code>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)])</code> || 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>]] || <code>I = z*(1 - z)* diff(+(1 - 2*z)* diff(-, z), [z$(2)])(1)/(4)</code> || <code>I == z*(1 - z)* D[+(1 - 2*z)* D[-, z], {z, 2}]Divide[1,4]</code> || 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>]] || <code>diff(f[1], z)+ f[1]*(f[2]- f[3])+ 2*mu[1] = 0</code> || <code>D[Subscript[f, 1], z]+ Subscript[f, 1]*(Subscript[f, 2]- Subscript[f, 3])+ 2*Subscript[\[Mu], 1] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.732050808+1.000000000*I <- {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}</code><br><code>-1.000000000+1.732050808*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.7320508075688774, 0.9999999999999999] <- {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]]]}</code><br><code>Complex[-0.9999999999999996, 1.7320508075688774] <- {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]]]}</code><br></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>]] || <code>diff(f[2], z)+ f[2]*(f[3]- f[1])+ 2*mu[2] = 0</code> || <code>D[Subscript[f, 2], z]+ Subscript[f, 2]*(Subscript[f, 3]- Subscript[f, 1])+ 2*Subscript[\[Mu], 2] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.732050808+1.000000000*I <- {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}</code><br><code>-1.000000000+1.732050808*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.7320508075688774, 0.9999999999999999] <- {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]]]}</code><br><code>Complex[-0.9999999999999996, 1.7320508075688774] <- {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]]]}</code><br></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>]] || <code>diff(f[3], z)+ f[3]*(f[1]- f[2])+ 2*mu[3] = 0</code> || <code>D[Subscript[f, 3], z]+ Subscript[f, 3]*(Subscript[f, 1]- Subscript[f, 2])+ 2*Subscript[\[Mu], 3] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.732050808+1.000000000*I <- {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}</code><br><code>-1.000000000+1.732050808*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.7320508075688774, 0.9999999999999999] <- {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]]]}</code><br><code>Complex[-0.9999999999999996, 1.7320508075688774] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.2.E16 32.2.E16] || [[Item:Q9172|<math>\mu_{1}+\mu_{2}+\mu_{3} = 1</math>]] || <code>mu[1]+ mu[2]+ mu[3] = 1</code> || <code>Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>f[1]*(z)+ f[2]*(z)+ f[3]*(z)+ 2*z = 0</code> || <code>Subscript[f, 1]*(z)+ Subscript[f, 2]*(z)+ Subscript[f, 3]*(z)+ 2*z == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2.E18 32.2.E18] || [[Item:Q9174|<math>(\alpha,\beta) = (\mu_{3}-\mu_{2},-2\mu_{1}^{2})</math>]] || <code>(alpha , beta) (mu[3]- mu[2], - 2*mu(mu[1])^(2))</code> || <code>(\[Alpha], \[Beta]) (Subscript[\[Mu], 3]- Subscript[\[Mu], 2], - 2*\[Mu](Subscript[\[Mu], 1])^(2))</code> || 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>]] || <code>z*diff(f[1], z) = f[1]*f[3]*(f[2]- f[4])+((1)/(2)- mu[3])* f[1]+ mu[1]*f[3]</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>298/300]: [[-.4330127020-.2500000000*I <- {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}</code><br><code>-1.799038106-.6160254036*I <- {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)}</code><br></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>]] || <code>z*diff(f[2], z) = f[2]*f[4]*(f[3]- f[1])+((1)/(2)- mu[4])* f[2]+ mu[2]*f[4]</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>298/300]: [[-.4330127020-.2500000000*I <- {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}</code><br><code>-1.799038106-.6160254036*I <- {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)}</code><br></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>]] || <code>z*diff(f[3], z) = f[3]*f[1]*(f[4]- f[2])+((1)/(2)- mu[1])* f[3]+ mu[3]*f[1]</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>298/300]: [[-.4330127020-.2500000000*I <- {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}</code><br><code>.9330127024+.1160254036*I <- {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)}</code><br></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>]] || <code>z*diff(f[4], z) = f[4]*f[2]*(f[1]- f[3])+((1)/(2)- mu[2])* f[4]+ mu[4]*f[2]</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>298/300]: [[-.4330127020-.2500000000*I <- {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}</code><br><code>.9330127024+.1160254036*I <- {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)}</code><br></div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/32.2.E20 32.2.E20] || [[Item:Q9179|<math>\mu_{1}+\mu_{2}+\mu_{3}+\mu_{4} = 1</math>]] || <code>mu[1]+ mu[2]+ mu[3]+ mu[4] = 1</code> || <code>Subscript[\[Mu], 1]+ Subscript[\[Mu], 2]+ Subscript[\[Mu], 3]+ Subscript[\[Mu], 4] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2.E21 32.2.E21] || [[Item:Q9180|<math>f_{1}(z)+f_{3}(z) = \sqrt{z}</math>]] || <code>f[1]*(z)+ f[3]*(z) = sqrt(z)</code> || <code>Subscript[f, 1]*(z)+ Subscript[f, 3]*(z) == Sqrt[z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2.E22 32.2.E22] || [[Item:Q9181|<math>f_{2}(z)+f_{4}(z) = \sqrt{z}</math>]] || <code>f[2]*(z)+ f[4]*(z) = sqrt(z)</code> || <code>Subscript[f, 2]*(z)+ Subscript[f, 4]*(z) == Sqrt[z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((1)/(2)*mu(mu[1])^(2), -(1)/(2)*mu(mu[3])^(2), mu[4]- mu[2], -(1)/(2))</code> || <code>(Divide[1,2]*\[Mu](Subscript[\[Mu], 1])^(2), -Divide[1,2]*\[Mu](Subscript[\[Mu], 3])^(2), Subscript[\[Mu], 4]- Subscript[\[Mu], 2], -Divide[1,2])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex10 32.2#Ex10] || [[Item:Q9185|<math>z = \epsilon^{2}\zeta-\frac{6}{\epsilon^{10}}</math>]] || <code>z = (epsilon)^(2)* zeta -(6)/((epsilon)^(10))</code> || <code>z == \[Epsilon]^(2)* \[Zeta]-Divide[6,\[Epsilon]^(10)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex11 32.2#Ex11] || [[Item:Q9186|<math>\alpha = \frac{4}{\epsilon^{15}}</math>]] || <code>alpha = (4)/((epsilon)^(15))</code> || <code>\[Alpha] == Divide[4,\[Epsilon]^(15)]</code> || 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>]] || <code>diff(W, [zeta$(2)]) = 6*(W)^(2)+ zeta + (epsilon)^(6)*(2*(W)^(3)+ zeta*W)</code> || <code>D[W, {\[Zeta], 2}] == 6*(W)^(2)+ \[Zeta]+ \[Epsilon]^(6)*(2*(W)^(3)+ \[Zeta]*W)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-4.366025408-8.562177830*I <- {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 1}</code><br><code>-35.86602547-189.1217784*I <- {W = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, epsilon = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-4.366025403784439, -8.56217782649107] <- {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]]]}</code><br><code>Complex[-35.86602540378445, -189.1217782649107] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.2#Ex12 32.2#Ex12] || [[Item:Q9189|<math>z = 1+\epsilon^{2}\zeta</math>]] || <code>z = 1 + (epsilon)^(2)* zeta</code> || <code>z == 1 + \[Epsilon]^(2)* \[Zeta]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex13 32.2#Ex13] || [[Item:Q9190|<math>\alpha = -\tfrac{1}{2}\epsilon^{-6}</math>]] || <code>alpha = -(1)/(2)*(epsilon)^(- 6)</code> || <code>\[Alpha] == -Divide[1,2]*\[Epsilon]^(- 6)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex14 32.2#Ex14] || [[Item:Q9191|<math>\beta = \tfrac{1}{2}\epsilon^{-6}+2a\epsilon^{-3}</math>]] || <code>beta = (1)/(2)*(epsilon)^(- 6)+ 2*a*(epsilon)^(- 3)</code> || <code>\[Beta] == Divide[1,2]*\[Epsilon]^(- 6)+ 2*a*\[Epsilon]^(- 3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex15 32.2#Ex15] || [[Item:Q9192|<math>\gamma = -\delta</math>]] || <code>gamma = - delta</code> || <code>\[Gamma] == - \[Delta]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex16 32.2#Ex16] || [[Item:Q9194|<math>z = 2^{-2/3}\epsilon\zeta-\epsilon^{-3}</math>]] || <code>z = (2)^(- 2/ 3)* epsilon*zeta - (epsilon)^(- 3)</code> || <code>z == (2)^(- 2/ 3)* \[Epsilon]*\[Zeta]- \[Epsilon]^(- 3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex17 32.2#Ex17] || [[Item:Q9195|<math>\alpha = -2a-\tfrac{1}{2}\epsilon^{-6}</math>]] || <code>alpha = - 2*a -(1)/(2)*(epsilon)^(- 6)</code> || <code>\[Alpha] == - 2*a -Divide[1,2]*\[Epsilon]^(- 6)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex18 32.2#Ex18] || [[Item:Q9196|<math>\beta = -\tfrac{1}{2}\epsilon^{-12}</math>]] || <code>beta = -(1)/(2)*(epsilon)^(- 12)</code> || <code>\[Beta] == -Divide[1,2]*\[Epsilon]^(- 12)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex19 32.2#Ex19] || [[Item:Q9198|<math>z = \zeta^{2}</math>]] || <code>z = (zeta)^(2)</code> || <code>z == \[Zeta]^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>alpha = (1)/(4)*a*(epsilon)^(- 1)+(1)/(8)*c*(epsilon)^(- 2)</code> || <code>\[Alpha] == Divide[1,4]*a*\[Epsilon]^(- 1)+Divide[1,8]*c*\[Epsilon]^(- 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex21 32.2#Ex21] || [[Item:Q9200|<math>\beta = -\tfrac{1}{8}c\epsilon^{-2}</math>]] || <code>beta = -(1)/(8)*c*(epsilon)^(- 2)</code> || <code>\[Beta] == -Divide[1,8]*c*\[Epsilon]^(- 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex22 32.2#Ex22] || [[Item:Q9201|<math>\gamma = \tfrac{1}{4}\epsilon b</math>]] || <code>gamma = (1)/(4)*epsilon*b</code> || <code>\[Gamma] == Divide[1,4]*\[Epsilon]*b</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex23 32.2#Ex23] || [[Item:Q9202|<math>\delta = \tfrac{1}{8}\epsilon^{2}d</math>]] || <code>delta = (1)/(8)*(epsilon)^(2)* d</code> || <code>\[Delta] == Divide[1,8]*\[Epsilon]^(2)* d</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex24 32.2#Ex24] || [[Item:Q9204|<math>z = 1+\sqrt{2}\epsilon\zeta</math>]] || <code>z = 1 +sqrt(2)*epsilon*zeta</code> || <code>z == 1 +Sqrt[2]*\[Epsilon]*\[Zeta]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex25 32.2#Ex25] || [[Item:Q9205|<math>\alpha = \tfrac{1}{2}\epsilon^{-4}</math>]] || <code>alpha = (1)/(2)*(epsilon)^(- 4)</code> || <code>\[Alpha] == Divide[1,2]*\[Epsilon]^(- 4)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex26 32.2#Ex26] || [[Item:Q9206|<math>\beta = \tfrac{1}{4}b</math>]] || <code>beta = (1)/(4)*b</code> || <code>\[Beta] == Divide[1,4]*b</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex27 32.2#Ex27] || [[Item:Q9207|<math>\gamma = -\epsilon^{-4}</math>]] || <code>gamma = - (epsilon)^(- 4)</code> || <code>\[Gamma] == - \[Epsilon]^(- 4)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex28 32.2#Ex28] || [[Item:Q9208|<math>\delta = a\epsilon^{-2}-\tfrac{1}{2}\epsilon^{-4}</math>]] || <code>delta = a*(epsilon)^(- 2)-(1)/(2)*(epsilon)^(- 4)</code> || <code>\[Delta] == a*\[Epsilon]^(- 2)-Divide[1,2]*\[Epsilon]^(- 4)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex29 32.2#Ex29] || [[Item:Q9210|<math>z = 1+\epsilon\zeta</math>]] || <code>z = 1 + epsilon*zeta</code> || <code>z == 1 + \[Epsilon]*\[Zeta]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex30 32.2#Ex30] || [[Item:Q9211|<math>\gamma = c\epsilon^{-1}-d\epsilon^{-2}</math>]] || <code>gamma = c*(epsilon)^(- 1)- d*(epsilon)^(- 2)</code> || <code>\[Gamma] == c*\[Epsilon]^(- 1)- d*\[Epsilon]^(- 2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.2#Ex31 32.2#Ex31] || [[Item:Q9212|<math>\delta = d\epsilon^{-2}</math>]] || <code>delta = d*(epsilon)^(- 2)</code> || <code>\[Delta] == d*\[Epsilon]^(- 2)</code> || 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>]] || <code>diff(u, [x$(2)]) = 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))* u</code> || <code>D[u, {x, 2}] == 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])* u</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[3.043949625-3.665224602*I <- {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>3.476962328-1.415224600*I <- {nu = 1/2*3^(1/2)+1/2*I, u = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[3.043949623616789, -3.6652245962155616] <- {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]]]}</code><br><code>Complex[1.67792421983235, -4.031249999999999] <- {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]]]}</code><br></div></div>
-|-
-| [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>]] || <code>w*(x) = 2*sqrt(2)*(u[k])^(2)*(sqrt(2)*x , nu)</code> || <code>w*(x) == 2*Sqrt[2]*(Subscript[u, k])^(2)*(Sqrt[2]*x , \[Nu])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(u)^(2) = -(1)/(3)*x +(1)/(6)*sqrt((x)^(2)+ 12*nu + 6)</code> || <code>(u)^(2) == -Divide[1,3]*x +Divide[1,6]*Sqrt[(x)^(2)+ 12*\[Nu]+ 6]</code> || 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>]] || <code>diff(Psi, lambda) = A*(z , lambda)* Psi</code> || <code>D[\[CapitalPsi], \[Lambda]] == A*(z , \[Lambda])* \[CapitalPsi]</code> || 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>]] || <code>diff(Psi, z) = B*(z , lambda)* Psi</code> || <code>D[\[CapitalPsi], z] == B*(z , \[Lambda])* \[CapitalPsi]</code> || 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>]] || <code>diff(A, z)- diff(B, lambda)+ A*B - B*A = 0</code> || <code>D[A, z]- D[B, \[Lambda]]+ A*B - B*A == 0</code> || Successful || Successful || - || Successful [Tested: 300]
-|-
-| [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>]] || <code>(alpha , beta , gamma , delta) = (2*theta[0], 2*(1 - theta[infinity]), 1 , - 1)</code> || <code>(\[Alpha], \[Beta], \[Gamma], \[Delta]) == (2*Subscript[\[Theta], 0], 2*(1 - Subscript[\[Theta], Infinity]), 1 , - 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>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])</code> || <code>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])</code> || 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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || Skipped - Because timed out || Error
-|-
-| [https://dlmf.nist.gov/32.5.E2 32.5.E2] || [[Item:Q9237|<math>w(z) = K(z,z)</math>]] || <code>w*(z) = K*(z , z)</code> || <code>w*(z) == K*(z , z)</code> || 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>]] || <code>diff(q, z) = diff(H, p)</code> || <code>D[q, z] == D[H, p]</code> || 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>]] || <code>diff(p, z) = - diff(H, q)</code> || <code>D[p, z] == - D[H, q]</code> || Successful || Successful || - || Successful [Tested: 300]
-|-
-| [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>]] || <code>(- 2*kappa[infinity]*theta[infinity], 2*kappa[0]*(theta[0]+ 1), kappa(kappa[infinity])^(2), - kappa(kappa[0])^(2))</code> || <code>(- 2*Subscript[\[Kappa], Infinity]*Subscript[\[Theta], Infinity], 2*Subscript[\[Kappa], 0]*(Subscript[\[Theta], 0]+ 1), \[Kappa](Subscript[\[Kappa], Infinity])^(2), - \[Kappa](Subscript[\[Kappa], 0])^(2))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(- 4*eta[infinity]*theta[infinity], 4*eta[0]*(theta[0]+ 1), 4*eta(eta[infinity])^(2), - 4*eta(eta[0])^(2))</code> || <code>(- 4*Subscript[\[Eta], Infinity]*Subscript[\[Theta], Infinity], 4*Subscript[\[Eta], 0]*(Subscript[\[Theta], 0]+ 1), 4*\[Eta](Subscript[\[Eta], Infinity])^(2), - 4*\[Eta](Subscript[\[Eta], 0])^(2))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha , beta , gamma , delta) (2*kappa[infinity], kappa[0]*(theta - 1), 0 , - kappa(kappa[0])^(2))</code> || <code>(\[Alpha], \[Beta], \[Gamma], \[Delta]) (2*Subscript[\[Kappa], Infinity], Subscript[\[Kappa], 0]*(\[Theta]- 1), 0 , - \[Kappa](Subscript[\[Kappa], 0])^(2))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha +(1)/(2))/(w[alpha + 1]+ w[alpha])+(alpha -(1)/(2))/(w[alpha]+ w[alpha - 1])+ 2*(w[alpha])^(2)+ z = 0</code> || <code>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</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[1], beta[1], gamma[1], delta[1]) = (- alpha[0], - beta[0], gamma[0], delta[0])</code> || <code>(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (- Subscript[\[Alpha], 0], - Subscript[\[Beta], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - delta[0], - gamma[0])</code> || <code>(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Delta], 0], - Subscript[\[Gamma], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex1 32.7#Ex1] || [[Item:Q9288|<math>\alpha_{1} = \alpha_{3}</math>]] || <code>alpha[1] = alpha[3]</code> || <code>Subscript[\[Alpha], 1] == Subscript[\[Alpha], 3]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex2 32.7#Ex2] || [[Item:Q9289|<math>\alpha_{2} = \alpha_{4}</math>]] || <code>alpha[2] = alpha[4]</code> || <code>Subscript[\[Alpha], 2] == Subscript[\[Alpha], 4]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex3 32.7#Ex3] || [[Item:Q9290|<math>\beta_{1} = \beta_{2}</math>]] || <code>beta[1] = beta[2]</code> || <code>Subscript[\[Beta], 1] == Subscript[\[Beta], 2]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex4 32.7#Ex4] || [[Item:Q9291|<math>\beta_{3} = \beta_{4}</math>]] || <code>beta[3] = beta[4]</code> || <code>Subscript[\[Beta], 3] == Subscript[\[Beta], 4]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex5 32.7#Ex5] || [[Item:Q9296|<math>\beta_{5} = \beta_{0}+2</math>]] || <code>beta[5] = beta[0]+ 2</code> || <code>Subscript[\[Beta], 5] == Subscript[\[Beta], 0]+ 2</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex6 32.7#Ex6] || [[Item:Q9297|<math>\beta_{6} = \beta_{0}-2</math>]] || <code>beta[6] = beta[0]- 2</code> || <code>Subscript[\[Beta], 6] == Subscript[\[Beta], 0]- 2</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex8 32.7#Ex8] || [[Item:Q9301|<math>z = \tfrac{1}{2}\zeta^{2}</math>]] || <code>z = (1)/(2)*(zeta)^(2)</code> || <code>z == Divide[1,2]*\[Zeta]^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[1])^(+) = (1)/(4)*(2 - 2*alpha[0]+ 3*sqrt(- 2*beta[0]))</code> || <code>(Subscript[\[Alpha], 1])^(+) == Divide[1,4]*(2 - 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(beta[1])^(+) = -(1)/(2)*(1 + alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</code> || <code>(Subscript[\[Beta], 1])^(+) == -Divide[1,2]*(1 + Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[2])^(+) = -(1)/(4)*(2 + 2*alpha[0]+ 3*sqrt(- 2*beta[0]))</code> || <code>(Subscript[\[Alpha], 2])^(+) == -Divide[1,4]*(2 + 2*Subscript[\[Alpha], 0]+ 3*Sqrt[- 2*Subscript[\[Beta], 0]])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(beta[2])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</code> || <code>(Subscript[\[Beta], 2])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[3])^(+) = (3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0])</code> || <code>(Subscript[\[Alpha], 3])^(+) == Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(beta[3])^(+) = -(1)/(2)*(1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</code> || <code>(Subscript[\[Beta], 3])^(+) == -Divide[1,2]*(1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[4])^(+) = -(3)/(2)-(1)/(2)*alpha[0]-(3)/(4)*sqrt(- 2*beta[0])</code> || <code>(Subscript[\[Alpha], 4])^(+) == -Divide[3,2]-Divide[1,2]*Subscript[\[Alpha], 0]-Divide[3,4]*Sqrt[- 2*Subscript[\[Beta], 0]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(beta[4])^(+) = -(1)/(2)*(- 1 - alpha[0]+(1)/(2)*sqrt(- 2*beta[0]))^(2)</code> || <code>(Subscript[\[Beta], 4])^(+) == -Divide[1,2]*(- 1 - Subscript[\[Alpha], 0]+Divide[1,2]*Sqrt[- 2*Subscript[\[Beta], 0]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex17 32.7#Ex17] || [[Item:Q9314|<math>z_{1} = -z_{0}</math>]] || <code>z[1] = - z[0]</code> || <code>Subscript[z, 1] == - Subscript[z, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex18 32.7#Ex18] || [[Item:Q9315|<math>z_{2} = z_{0}</math>]] || <code>z[2] = z[0]</code> || <code>Subscript[z, 2] == Subscript[z, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - gamma[0], delta[0])</code> || <code>(Subscript[\[Alpha], 1], Subscript[\[Beta], 1], Subscript[\[Gamma], 1], Subscript[\[Delta], 1]) == (Subscript[\[Alpha], 0], Subscript[\[Beta], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[2], beta[2], gamma[2], delta[2]) = (- beta[0], - alpha[0], - gamma[0], delta[0])</code> || <code>(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>alpha[1] = (1)/(8)*(gamma[0]+ varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2)</code> || <code>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)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>beta[1] = -(1)/(8)*(gamma[0]- varepsilon[1]*(1 - varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0])))^(2)</code> || <code>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)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>gamma[1] = varepsilon[1]*(varepsilon[3]*sqrt(- 2*beta[0])- varepsilon[2]*sqrt(2*alpha[0]))</code> || <code>Subscript[\[Gamma], 1] == Subscript[\[CurlyEpsilon], 1]*(Subscript[\[CurlyEpsilon], 3]*Sqrt[- 2*Subscript[\[Beta], 0]]- Subscript[\[CurlyEpsilon], 2]*Sqrt[2*Subscript[\[Alpha], 0]])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex25 32.7#Ex25] || [[Item:Q9327|<math>z = \sqrt{2\zeta}</math>]] || <code>z = sqrt(2*zeta)</code> || <code>z == Sqrt[2*\[Zeta]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[0], beta[0], gamma[0], delta[0]) = ((beta - varepsilon*alpha + 2)^(2)/ 32 , -(beta + varepsilon*alpha - 2)^(2)/ 32 , - varepsilon , 0)</code> || <code>(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)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7.E33 32.7.E33] || [[Item:Q9329|<math>z_{1} = 1/z_{0}</math>]] || <code>z[1] = 1/ z[0]</code> || <code>Subscript[z, 1] == 1/ Subscript[z, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7.E34 32.7.E34] || [[Item:Q9330|<math>z_{2} = 1-z_{0}</math>]] || <code>z[2] = 1 - z[0]</code> || <code>Subscript[z, 2] == 1 - Subscript[z, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7.E35 32.7.E35] || [[Item:Q9331|<math>z_{3} = 1/z_{0}</math>]] || <code>z[3] = 1/ z[0]</code> || <code>Subscript[z, 3] == 1/ Subscript[z, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[1], beta[1], gamma[1], delta[1]) = (alpha[0], beta[0], - delta[0]+(1)/(2), - gamma[0]+(1)/(2))</code> || <code>(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])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[2], beta[2], gamma[2], delta[2]) = (alpha[0], - gamma[0], - beta[0], delta[0])</code> || <code>(Subscript[\[Alpha], 2], Subscript[\[Beta], 2], Subscript[\[Gamma], 2], Subscript[\[Delta], 2]) == (Subscript[\[Alpha], 0], - Subscript[\[Gamma], 0], - Subscript[\[Beta], 0], Subscript[\[Delta], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha[3], beta[3], gamma[3], delta[3]) = (- beta[0], - alpha[0], gamma[0], delta[0])</code> || <code>(Subscript[\[Alpha], 3], Subscript[\[Beta], 3], Subscript[\[Gamma], 3], Subscript[\[Delta], 3]) == (- Subscript[\[Beta], 0], - Subscript[\[Alpha], 0], Subscript[\[Gamma], 0], Subscript[\[Delta], 0])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((1)/(2)*(theta[infinity]- 1)^(2), -(1)/(2)*theta(theta[0])^(2),(1)/(2)*theta(theta[1])^(2),(1)/(2)*(1 - theta(theta[2])^(2)))</code> || <code>(Divide[1,2]*(Subscript[\[Theta], Infinity]- 1)^(2), -Divide[1,2]*\[Theta](Subscript[\[Theta], 0])^(2),Divide[1,2]*\[Theta](Subscript[\[Theta], 1])^(2),Divide[1,2]*(1 - \[Theta](Subscript[\[Theta], 2])^(2)))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>((1)/(2)*(Theta[infinity]- 1)^(2), -(1)/(2)*Theta(Theta[0])^(2),(1)/(2)*Theta(Theta[1])^(2),(1)/(2)*(1 - Theta(Theta[2])^(2)))</code> || <code>(Divide[1,2]*(Subscript[\[CapitalTheta], Infinity]- 1)^(2), -Divide[1,2]*\[CapitalTheta](Subscript[\[CapitalTheta], 0])^(2),Divide[1,2]*\[CapitalTheta](Subscript[\[CapitalTheta], 1])^(2),Divide[1,2]*(1 - \[CapitalTheta](Subscript[\[CapitalTheta], 2])^(2)))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7.E44 32.7.E44] || [[Item:Q9340|<math>\theta_{j} = \Theta_{j}+\tfrac{1}{2}\sigma</math>]] || <code>theta[j] = Theta[j]+(1)/(2)*sigma</code> || <code>Subscript[\[Theta], j] == Subscript[\[CapitalTheta], j]+Divide[1,2]*\[Sigma]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7.E45 32.7.E45] || [[Item:Q9341|<math>\sigma = \theta_{0}+\theta_{1}+\theta_{2}+\theta_{\infty}-1</math>]] || <code>sigma = theta[0]+ theta[1]+ theta[2]+ theta[infinity]- 1</code> || <code>\[Sigma] == Subscript[\[Theta], 0]+ Subscript[\[Theta], 1]+ Subscript[\[Theta], 2]+ Subscript[\[Theta], Infinity]- 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>u[1]*(zeta[1]) = ((1 - w)*(w - z))/((1 +sqrt(z))^(2)* w)</code> || <code>Subscript[u, 1]*(Subscript[\[Zeta], 1]) == Divide[(1 - w)*(w - z),(1 +Sqrt[z])^(2)* w]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>zeta[1] = ((1 -sqrt(z))/(1 +sqrt(z)))^(2)</code> || <code>Subscript[\[Zeta], 1] == (Divide[1 -Sqrt[z],1 +Sqrt[z]])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>u[2]*(zeta[2]) = (((w)^(2)- z)^(2))/(4*w*(w - 1)*(w - z))</code> || <code>Subscript[u, 2]*(Subscript[\[Zeta], 2]) == Divide[((w)^(2)- z)^(2),4*w*(w - 1)*(w - z)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.7#Ex29 32.7#Ex29] || [[Item:Q9346|<math>\zeta_{2} = z</math>]] || <code>zeta[2] = z</code> || <code>Subscript[\[Zeta], 2] == z</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>u[3]*(zeta[3]) = ((1 - (z)^(1/ 4))/(1 + (z)^(1/ 4)))^(2)*((sqrt(w)+ (z)^(1/ 4))/(sqrt(w)- (z)^(1/ 4)))^(2)</code> || <code>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)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>zeta[3] = ((1 - (z)^(1/ 4))/(1 + (z)^(1/ 4)))^(4)</code> || <code>Subscript[\[Zeta], 3] == (Divide[1 - (z)^(1/ 4),1 + (z)^(1/ 4)])^(4)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex1 32.8#Ex1] || [[Item:Q9355|<math>Q_{2}(z) = z^{3}+4</math>]] || <code>Q[2]*(z) = (z)^(3)+ 4</code> || <code>Subscript[Q, 2]*(z) == (z)^(3)+ 4</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex2 32.8#Ex2] || [[Item:Q9356|<math>Q_{3}(z) = z^{6}+20z^{3}-80</math>]] || <code>Q[3]*(z) = (z)^(6)+ 20*(z)^(3)- 80</code> || <code>Subscript[Q, 3]*(z) == (z)^(6)+ 20*(z)^(3)- 80</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex3 32.8#Ex3] || [[Item:Q9357|<math>Q_{4}(z) = z^{10}+60z^{7}+11200z</math>]] || <code>Q[4]*(z) = (z)^(10)+ 60*(z)^(7)+ 11200*z</code> || <code>Subscript[Q, 4]*(z) == (z)^(10)+ 60*(z)^(7)+ 11200*z</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>Q[5]*(z) = (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000</code> || <code>Subscript[Q, 5]*(z) == (z)^(15)+ 140*(z)^(12)+ 2800*(z)^(9)+ 78400*(z)^(6)- 313600*(z)^(3)- 6272000</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>Q[6]*(z) = (z)^(21)+ 280*(z)^(18)+ 18480*(z)^(15)+ 627200*(z)^(12)- 17248000*(z)^(9)+ 1448832000*(z)^(6)+ 19317760000*(z)^(3)- 38635520000</code> || <code>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</code> || 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>]] || <code>sum(p[m]*(z)* (lambda)^(m), m = 0..infinity) = exp(z*lambda -(4)/(3)*(lambda)^(3))</code> || <code>Sum[Subscript[p, m]*(z)* \[Lambda]^(m), {m, 0, Infinity}, GenerateConditions->None] == Exp[z*\[Lambda]-Divide[4,3]*\[Lambda]^(3)]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{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]] <- {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]]]}</code><br><code>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]] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.8.E14 32.8.E14] || [[Item:Q9366|<math>\alpha+\beta = 4n</math>]] || <code>alpha + beta = 4*n</code> || <code>\[Alpha]+ \[Beta] == 4*n</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8.E15 32.8.E15] || [[Item:Q9367|<math>w(z) = \ifrac{P_{m}(z)}{Q_{m}(z)}</math>]] || <code>w*(z) = (P[m]*(z))/(Q[m]*(z))</code> || <code>w*(z) == Divide[Subscript[P, m]*(z),Subscript[Q, m]*(z)]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex6 32.8#Ex6] || [[Item:Q9374|<math>\alpha = m</math>]] || <code>alpha = m</code> || <code>\[Alpha] == m</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex7 32.8#Ex7] || [[Item:Q9375|<math>\beta = -2(1+2n-m)^{2}</math>]] || <code>beta = - 2*(1 + 2*n - m)^(2)</code> || <code>\[Beta] == - 2*(1 + 2*n - m)^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex8 32.8#Ex8] || [[Item:Q9376|<math>\mspace{12.0mu }\alpha = m</math>]] || <code>alpha = m</code> || <code>\[Alpha] == m</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8#Ex9 32.8#Ex9] || [[Item:Q9377|<math>\beta = -2(\tfrac{1}{3}+2n-m)^{2}</math>]] || <code>beta = - 2*((1)/(3)+ 2*n - m)^(2)</code> || <code>\[Beta] == - 2*(Divide[1,3]+ 2*n - m)^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>w*(z) = lambda*z + mu +((P[n - 1]*(z))/(Q[n]*(z)))</code> || <code>w*(z) == \[Lambda]*z + \[Mu]+(Divide[Subscript[P, n - 1]*(z),Subscript[Q, n]*(z)])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.8.E33 32.8.E33] || [[Item:Q9387|<math>a+b+c+d = 2n+1</math>]] || <code>a + b + c + d = 2*n + 1</code> || <code>a + b + c + d == 2*n + 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.9.E4 32.9.E4] || [[Item:Q9391|<math>\beta = 2n</math>]] || <code>beta = 2*n</code> || <code>\[Beta] == 2*n</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>w*(z) = (P[(n)^(2)+ 1]*(zeta))/(Q[(n)^(2)]*(zeta))</code> || <code>w*(z) == Divide[Subscript[P, (n)^(2)+ 1]*(\[Zeta]),Subscript[Q, (n)^(2)]*(\[Zeta])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha , beta , gamma) = ((1)/(2)*(mu)^(2), -(1)/(8)*(2*n - 1)^(2), - 1)</code> || <code>(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,2]*\[Mu]^(2), -Divide[1,8]*(2*n - 1)^(2), - 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(alpha , beta , gamma) = ((1)/(8)*(2*n - 1)^(2), -(1)/(2)*(mu)^(2), 1)</code> || <code>(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,8]*(2*n - 1)^(2), -Divide[1,2]*\[Mu]^(2), 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>w*(z) = (P[(n)^(2)- n + 1]*(zeta))/(Q[(n)^(2)- n]*(zeta))</code> || <code>w*(z) == Divide[Subscript[P, (n)^(2)- n + 1]*(\[Zeta]),Subscript[Q, (n)^(2)- n]*(\[Zeta])]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.10.E2 32.10.E2] || [[Item:Q9402|<math>\alpha = n+\tfrac{1}{2}</math>]] || <code>alpha = n +(1)/(2)</code> || <code>\[Alpha] == n +Divide[1,2]</code> || 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>]] || <code>phi*(z) = C[1]*AiryAi(- (2)^(- 1/ 3)* z)+ C[2]*AiryBi(- (2)^(- 1/ 3)* z)</code> || <code>\[Phi]*(z) == Subscript[C, 1]*AiryAi[- (2)^(- 1/ 3)* z]+ Subscript[C, 2]*AiryBi[- (2)^(- 1/ 3)* z]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.2986692739+.5787509238*I <- {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}</code><br><code>.3018910357e-1+.1740730853*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.29866927421000106, 0.5787509234724151] <- {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]]]}</code><br><code>Complex[0.03018910341830547, 0.174073084997731] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.10.E11 32.10.E11] || [[Item:Q9411|<math>\varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2</math>]] || <code>varepsilon[1]*alpha + varepsilon[2]*beta = 4*n + 2</code> || <code>Subscript[\[CurlyEpsilon], 1]*\[Alpha]+ Subscript[\[CurlyEpsilon], 2]*\[Beta] == 4*n + 2</code> || 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>]] || <code>phi*(z) = (z)^(nu)*(C[1]*BesselJ(nu, zeta)+ C[2]*BesselY(nu, zeta))</code> || <code>\[Phi]*(z) == (z)^\[Nu]*(Subscript[C, 1]*BesselJ[\[Nu], \[Zeta]]+ Subscript[C, 2]*BesselY[\[Nu], \[Zeta]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.6857713611+1.049278090*I <- {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}</code><br><code>-.1639325500+1.038275666*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.6857713606630202, 1.0492780901981935] <- {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]]]}</code><br><code>Complex[-0.16393255022963316, 1.0382756660889538] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.10.E15 32.10.E15] || [[Item:Q9415|<math>\beta = -2(2n+1+\varepsilon\alpha)^{2}</math>]] || <code>beta = - 2*(2*n + 1 + varepsilon*alpha)^(2)</code> || <code>\[Beta] == - 2*(2*n + 1 + \[CurlyEpsilon]*\[Alpha])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.10.E16 32.10.E16] || [[Item:Q9416|<math>\beta = -2n^{2}</math>]] || <code>beta = - 2*(n)^(2)</code> || <code>\[Beta] == - 2*(n)^(2)</code> || 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>]] || <code>phi*(z) = (C[1]*CylinderU(a, sqrt(2)*z)+ C[2]*CylinderV(a, sqrt(2)*z))* exp((1)/(2)*varepsilon*(z)^(2))</code> || <code>\[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)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.6213533818-.8057984780*I <- {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}</code><br><code>1.542195596-1.017130546*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{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]]]]] <- {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]]]}</code><br><code>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]]]]] <- {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, </div></div>
-|-
-| [https://dlmf.nist.gov/32.10.E23 32.10.E23] || [[Item:Q9423|<math>a+b+\varepsilon_{3}\gamma = 2n+1</math>]] || <code>a + b + varepsilon[3]*gamma = 2*n + 1</code> || <code>a + b + Subscript[\[CurlyEpsilon], 3]*\[Gamma] == 2*n + 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.10.E24 32.10.E24] || [[Item:Q9424|<math>(a-n)(b-n) = 0</math>]] || <code>(a - n)*(b - n) = 0</code> || <code>(a - n)*(b - n) == 0</code> || 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>]] || <code>phi*(z) = (C[1]*WhittakerM(kappa, mu, zeta)+ C[2]*WhittakerW(kappa, mu, zeta))/((zeta)^((a - b + 1)/ 2))*exp((1)/(2)*zeta)</code> || <code>\[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]]</code> || Failure || Failure || Manual Skip! || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/32.10.E28 32.10.E28] || [[Item:Q9428|<math>a+b+c+d = 2n+1</math>]] || <code>a + b + c + d = 2*n + 1</code> || <code>a + b + c + d == 2*n + 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.10#Ex1 32.10#Ex1] || [[Item:Q9430|<math>w(z) = \frac{\zeta-1}{a\phi(\zeta)}\deriv{\phi}{\zeta}</math>]] || <code>w*(z) = (zeta - 1)/(a*phi*(zeta))*diff(phi, zeta)</code> || <code>w*(z) == Divide[\[Zeta]- 1,a*\[Phi]*(\[Zeta])]*D[\[Phi], \[Zeta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5000000004+.8660254040*I <- {a = -3/2, phi = 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, zeta = 1/2*3^(1/2)+1/2*I}</code><br><code>.5000000004+.8660254040*I <- {a = -3/2, phi = 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, zeta = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.10#Ex2 32.10#Ex2] || [[Item:Q9431|<math>\zeta = \frac{1}{1-z}</math>]] || <code>zeta = (1)/(1 - z)</code> || <code>\[Zeta] == Divide[1,1 - z]</code> || 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>]] || <code>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)</code> || <code>\[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]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[Float(infinity)+Float(infinity)*I <- {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}</code><br><code>Float(infinity)+Float(infinity)*I <- {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)}</code><br></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>]] || <code>u = int((1)/(sqrt(t*(t - 1)*(t - z))), t = 0..Lambda)</code> || <code>u == Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, 0, \[CapitalLambda]}, GenerateConditions->None]</code> || 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>]] || <code>z*(1 - z)* diff(phi, [z$(2)])+(1 - 2*z)* diff(phi, z)-(1)/(4)*phi = 0</code> || <code>z*(1 - z)* D[\[Phi], {z, 2}]+(1 - 2*z)* D[\[Phi], z]-Divide[1,4]*\[Phi] == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>70/70]: [[-.2165063510-.1250000000*I <- {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.2165063510-.1250000000*I <- {phi = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[-0.21650635094610968, -0.12499999999999999] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.12499999999999994, -0.21650635094610968] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/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>]] || <code>phi*(x) = (24)^(1/ 4)*((4)/(5)*(abs(x))^(5/ 4)-(5)/(8)*(d)^(2)* ln(abs(x)))</code> || <code>\[Phi]*(x) == (24)^(1/ 4)*(Divide[4,5]*(Abs[x])^(5/ 4)-Divide[5,8]*(d)^(2)* Log[Abs[x]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-1.359899020+1.235754628*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>-.7909045934-.5804030210*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.3598990205302544, 1.2357546278215892] <- {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]]]}</code><br><code>Complex[-3.408937126206912, 1.7847927334982474] <- {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]]]}</code><br></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>]] || <code>phi*(x) = (2)/(3)*(abs(x))^(3/ 2)-(3)/(4)*(d)^(2)* ln(abs(x))</code> || <code>\[Phi]*(x) == Divide[2,3]*(Abs[x])^(3/ 2)-Divide[3,4]*(d)^(2)* Log[Abs[x]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.2263426496+1.013357313*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>-.626197514e-1-.2002123003*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.22634264982563074, 1.0133573129774054] <- {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]]]}</code><br><code>Complex[-1.8226954558510269, 1.5623954186540636] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.11.E8 32.11.E8] || [[Item:Q9443|<math>d^{2} = -\pi^{-1}\ln@{1-k^{2}}</math>]] || <code>(d)^(2) = - (Pi)^(- 1)* ln(1 - (k)^(2))</code> || <code>(d)^(2) == - (Pi)^(- 1)* Log[1 - (k)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 1}</code><br><code>.8496991530+1.866025404*I <- {d = 1/2*3^(1/2)+1/2*I, k = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}</code><br><code>Complex[0.84969915256606, 1.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]}</code><br></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>]] || <code>theta[0] = (3)/(2)*(d)^(2)* ln(2)+ argument(GAMMA(1 -(1)/(2)*I*(d)^(2)))+(1)/(4)*Pi*(1 - 2*signum(k))</code> || <code>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])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.126938891-.4004246008*I <- {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}</code><br><code>1.126938891-.4004246008*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.1269388909194178, -0.4004246003897078] <- {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]]]}</code><br><code>Complex[1.1269388909194178, -0.4004246003897078] <- {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]]]}</code><br></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>]] || <code>phi*(x) = (2)/(3)*(abs(x))^(3/ 2)+(3)/(4)*(d)^(2)* ln(abs(x))</code> || <code>\[Phi]*(x) == Divide[2,3]*(Abs[x])^(3/ 2)+Divide[3,4]*(d)^(2)* Log[Abs[x]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.777561816e-1+.4866426869*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>.4572406346+.7002123003*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.0777561812554926, 0.48664268702259433] <- {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]]]}</code><br><code>Complex[-2.1267942869321503, 1.0356807926992524] <- {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]]]}</code><br></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>]] || <code>chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) = n*Pi</code> || <code>\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] == n*Pi</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><code>60/60]: [[-4.109048867-.4004246008*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 1}</code><br><code>-7.250641521-.4004246008*I <- {chi = 1/2*3^(1/2)+1/2*I, d = -1/2+1/2*I*3^(1/2), n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><code>{Complex[-4.10904886506357, -0.4004246003897078] <- {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]]]}</code><br><code>Complex[-7.250641518653364, -0.4004246003897078] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.11.E17 32.11.E17] || [[Item:Q9452|<math>d^{2} = \pi^{-1}\ln@{1+k^{2}}</math>]] || <code>(d)^(2) = (Pi)^(- 1)* ln(1 + (k)^(2))</code> || <code>(d)^(2) == (Pi)^(- 1)* Log[1 + (k)^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[.2793644003+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 1}</code><br><code>-.122999981e-1+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, k = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.2793643998473485, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1]}</code><br><code>Complex[-0.012299998726776007, 0.8660254037844386] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2]}</code><br></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>]] || <code>chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2))) <> n*Pi</code> || <code>\[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]] \[NotEqual]n*Pi</code> || Failure || Failure || Successful [Tested: 60] || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 1.0]]] <- {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]]]}</code><br><code>Plus[Complex[-0.4392331450329683, -0.4004246003897078], Times[-3.141592653589793, StringJoin[0.5282230664408086, 2.0]]] <- {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]]]}</code><br></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>]] || <code>psi*(x) = (2)/(3)*sqrt(2)*(x)^(3/ 2)-(3)/(2)*(rho)^(2)* ln(x)</code> || <code>\[Psi]*(x) == Divide[2,3]*Sqrt[2]*(x)^(3/ 2)-Divide[3,2]*\[Rho]^(2)* Log[x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.1289138697+1.276714626*I <- {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>-.4201810172-.6504246006*I <- {psi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.12891387081109584, 1.276714625954811] <- {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]]]}</code><br><code>Complex[-2.1779519764877535, 1.8257527316314692] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.11.E21 32.11.E21] || [[Item:Q9456|<math>\sigma = -\sign@{\imagpart@@{s}}</math>]] || <code>sigma = - signum(Im(s))</code> || <code>\[Sigma] == - Sign[Im[s]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><code>200/200]: [[-.1339745960+.5000000000*I <- {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}</code><br><code>-1.500000000+.8660254040*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><code>{Complex[-0.1339745962155613, 0.49999999999999994] <- {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]]]}</code><br><code>Complex[1.8660254037844388, 0.49999999999999994] <- {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]]]}</code><br></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>]] || <code>(rho)^(2) = (Pi)^(- 1)* ln((1 +(abs(s))^(2))/abs(2*Im(s)))</code> || <code>\[Rho]^(2) == (Pi)^(- 1)* Log[(1 +(Abs[s])^(2))/Abs[2*Im[s]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><code>200/200]: [[.2989013521+.8660254040*I <- {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}</code><br><code>-.7010986487-.8660254040*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [200 / 200]<div class="mw-collapsible-content"><code>{Complex[0.2989013519411052, 0.8660254037844386] <- {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]]]}</code><br><code>Complex[0.3675975407110632, 0.8660254037844386] <- {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]]]}</code><br></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>]] || <code>theta = -(3)/(4)*Pi -(7)/(2)*(rho)^(2)* ln(2)+ argument(1 + (s)^(2))+ argument(GAMMA(I*(rho)^(2)))</code> || <code>\[Theta] == -Divide[3,4]*Pi -Divide[7,2]*\[Rho]^(2)* Log[2]+ Arg[1 + (s)^(2)]+ Arg[Gamma[I*\[Rho]^(2)]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.925696688-1.600990735*I <- {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}</code><br><code>.5596712830-1.234965331*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.6978889663556802, -1.6009907342426515] <- {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]]]}</code><br><code>Complex[2.496658442211441, -1.6009907342426515] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.11.E27 32.11.E27] || [[Item:Q9462|<math>\sigma = (2/\pi)\asin@{\pi\lambda}</math>]] || <code>sigma = (2/ Pi)* arcsin(Pi*lambda)</code> || <code>\[Sigma] == (2/ Pi)* ArcSin[Pi*\[Lambda]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><code>100/100]: [[.2138525505-.6623078870*I <- {lambda = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.152172854-.2962824830*I <- {lambda = 1/2*3^(1/2)+1/2*I, sigma = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><code>{Complex[0.2138525499640901, -0.6623078873679977] <- {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-1.1521728538203484, -0.296282483583559] <- {Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>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))</code> || <code>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]]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[3.808977659-.2371191295*I <- {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}</code><br><code>.9147008442+.353764288e-1*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[3.808977656026658, -0.23711913260929035] <- {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]]]}</code><br><code>Complex[0.914700843688173, 0.035376428936519655] <- {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]]]}</code><br></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>]] || <code>(h)^(*) = (1)/((Pi)^(1/ 2)* GAMMA(nu + 1))</code> || <code>(h)^(*) == Divide[1,(Pi)^(1/ 2)* Gamma[\[Nu]+ 1]]</code> || 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>]] || <code>phi*(x) = (1)/(3)*sqrt(3)*(x)^(2)-(4)/(3)*(d)^(2)*sqrt(3)*ln(sqrt(2)*abs(x))</code> || <code>\[Phi]*(x) == Divide[1,3]*Sqrt[3]*(x)^(2)-Divide[4,3]*(d)^(2)*Sqrt[3]*Log[Sqrt[2]*Abs[x]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8683794902+2.254077396*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}</code><br><code>-.1115135772-.4431471813*I <- {d = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 1/2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.8683794899108137, 2.2540773967762746] <- {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]]]}</code><br><code>Complex[-1.180658615765844, 2.8031155024529326] <- {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]]]}</code><br></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>]] || <code>(d)^(2) = -(1)/(4)*sqrt(3)*(Pi)^(- 1)* ln(1 -(abs(mu))^(2))</code> || <code>(d)^(2) == -Divide[1,4]*Sqrt[3]*(Pi)^(- 1)* Log[1 -(Abs[\[Mu]])^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><code>100/100]: [[Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I}</code><br><code>Float(-infinity)+.8660254040*I <- {d = 1/2*3^(1/2)+1/2*I, mu = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><code>{DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>DirectedInfinity[-1] <- {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>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)))</code> || <code>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)]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-3.888102442-1.096503697*I <- {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}</code><br><code>-5.254127846-.7304782927*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-3.888102439563878, -1.0965036955306524] <- {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]]]}</code><br><code>Complex[-5.254127843348316, -0.7304782917462136] <- {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]]]}</code><br></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>]] || <code>mu = 1 +((2*I*h*(Pi)^(3/ 2)* exp(- I*Pi*nu))/(GAMMA(- nu)))</code> || <code>\[Mu] == 1 +(Divide[2*I*h*(Pi)^(3/ 2)* Exp[- I*Pi*\[Nu]],Gamma[- \[Nu]]])</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[241.2310915-105.5149067*I <- {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)}</code><br><code>-1.289758519+2.890481636*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[241.23109103950634, -105.514906477147] <- {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]]]}</code><br><code>Complex[-1.289758518042884, 2.89048163412207] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.13.E1 32.13.E1] || [[Item:Q9474|<math>v_{t}-6v^{2}v_{x}+v_{xxx} = 0</math>]] || <code>v[t]- 6*(v)^(2)* v[x]+ v[x*x*x] = 0</code> || <code>Subscript[v, t]- 6*(v)^(2)* Subscript[v, x]+ Subscript[v, x*x*x] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex1 32.13#Ex1] || [[Item:Q9475|<math>z = x(3t)^{-1/3}</math>]] || <code>(x + y*I) = x*(3*t)^(- 1/ 3)</code> || <code>(x + y*I) == x*(3*t)^(- 1/ 3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex2 32.13#Ex2] || [[Item:Q9476|<math>v(x,t) = (3t)^{-1/3}w(z)</math>]] || <code>v*(x , t) = (3*t)^(- 1/ 3)* w*((x + y*I))</code> || <code>v*(x , t) == (3*t)^(- 1/ 3)* w*((x + y*I))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13.E3 32.13.E3] || [[Item:Q9477|<math>u_{t}+6uu_{x}+u_{xxx} = 0</math>]] || <code>u[t]+ 6*u*u[x]+ u[x*x*x] = 0</code> || <code>Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x*x*x] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex3 32.13#Ex3] || [[Item:Q9478|<math>z = x(3t)^{-1/3}</math>]] || <code>(x + y*I) = x*(3*t)^(- 1/ 3)</code> || <code>(x + y*I) == x*(3*t)^(- 1/ 3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex5 32.13#Ex5] || [[Item:Q9480|<math>z = x+3\lambda t^{2}</math>]] || <code>(x + y*I) = x + 3*lambda*(t)^(2)</code> || <code>(x + y*I) == x + 3*\[Lambda]*(t)^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex6 32.13#Ex6] || [[Item:Q9481|<math>u(x,t) = W(z)-\lambda t</math>]] || <code>u*(x , t) = W*((x + y*I))- lambda*t</code> || <code>u*(x , t) == W*((x + y*I))- \[Lambda]*t</code> || 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>]] || <code>u[x*t] = sin(u)</code> || <code>Subscript[u, x*t] == Sin[u]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.70450695e-2+.1624035369*I <- {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}</code><br><code>-1.358980334+.5284289409*I <- {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)}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.007045069484300837, 0.16240353677712993] <- {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]]]}</code><br><code>Complex[-1.3589803343001376, 0.5284289405615687] <- {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]]]}</code><br></div></div>
-|-
-| [https://dlmf.nist.gov/32.13#Ex7 32.13#Ex7] || [[Item:Q9483|<math>z = xt</math>]] || <code>(x + y*I) = x*t</code> || <code>(x + y*I) == x*t</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex8 32.13#Ex8] || [[Item:Q9484|<math>u(x,t) = v(z)</math>]] || <code>u*(x , t) = v*((x + y*I))</code> || <code>u*(x , t) == v*((x + y*I))</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13.E8 32.13.E8] || [[Item:Q9485|<math>u_{tt} = u_{xx}-6(u^{2})_{xx}+u_{xxxx}</math>]] || <code>u[t*t] = u[x*x]- 6*(u)^(2)[x*x]+ u[x*x*x*x]</code> || <code>Subscript[u, t*t] == Subscript[u, x*x]- 6*Subscript[(u)^(2), x*x]+ Subscript[u, x*x*x*x]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex9 32.13#Ex9] || [[Item:Q9486|<math>z = x-ct</math>]] || <code>(x + y*I) = x - c*t</code> || <code>(x + y*I) == x - c*t</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/32.13#Ex10 32.13#Ex10] || [[Item:Q9487|<math>u(x,t) = v(z)</math>]] || <code>u*(x , t) = v*((x + y*I))</code> || <code>u*(x , t) == v*((x + y*I))</code> || 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>]] || <code>int(exp(-(1)/(4)*(xi)^(4)- z*(xi)^(2))*p[m]*(xi)* p[n]*(xi), xi = - infinity..infinity) = KroneckerDelta[m, n]</code> || <code>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]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.5089051774+.3195154069*I <- {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}</code><br><code>.4910948226+.3195154069*I <- {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}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.5089051767265081, 0.31951540648426185] <- {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]]]}</code><br><code>Complex[0.49109482327349185, 0.31951540648426185] <- {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]]]}</code><br></div></div>
-|-
-| [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>]] || <code>a[n + 1]*(z)* p[n + 1]*(xi) = xi*p[n]*(xi)- a[n]*(z)* p[n - 1]*(xi)</code> || <code>Subscript[a, n + 1]*(z)* Subscript[p, n + 1]*(\[Xi]) == \[Xi]*Subscript[p, n]*(\[Xi])- Subscript[a, n]*(z)* Subscript[p, n - 1]*(\[Xi])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [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>]] || <code>(u[n + 1]+ u[n]+ u[n - 1])* u[n] = n - 2*z*u[n]</code> || <code>(Subscript[u, n + 1]+ Subscript[u, n]+ Subscript[u, n - 1])* Subscript[u, n] == n - 2*z*Subscript[u, n]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-|}

Results of Painlevé Transcendents: Difference between revisions

Latest revision as of 18:55, 25 May 2021

Navigation menu

Search