Results of Spheroidal Wave Functions: Difference between revisions

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Notation: 30.1 Special Notation
Properties: 30.2 Differential Equations
30.3 Eigenvalues
30.4 Functions of the First Kind
30.5 Functions of the Second Kind
30.6 Functions of Complex Argument
30.7 Graphics
30.8 Expansions in Series of Ferrers Functions
30.9 Asymptotic Approximations and Expansions
30.10 Series and Integrals
30.11 Radial Spheroidal Wave Functions
30.12 Generalized and Coulomb Spheroidal Functions
Applications: 30.13 Wave Equation in Prolate Spheroidal Coordinates
30.14 Wave Equation in Oblate Spheroidal Coordinates
30.15 Signal Analysis
Computation: 30.16 Methods of Computation
30.17 Tables
30.18 Software

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+<div style="-moz-column-count:2; column-count:2;">
-{| class="wikitable sortable" style="margin: 0;"
+; Notation : [[30.1|30.1 Special Notation]]<br>
-|-
+; Properties : [[30.2|30.2 Differential Equations]]<br>[[30.3|30.3 Eigenvalues]]<br>[[30.4|30.4 Functions of the First Kind]]<br>[[30.5|30.5 Functions of the Second Kind]]<br>[[30.6|30.6 Functions of Complex Argument]]<br>[[30.7|30.7 Graphics]]<br>[[30.8|30.8 Expansions in Series of Ferrers Functions]]<br>[[30.9|30.9 Asymptotic Approximations and Expansions]]<br>[[30.10|30.10 Series and Integrals]]<br>[[30.11|30.11 Radial Spheroidal Wave Functions]]<br>[[30.12|30.12 Generalized and Coulomb Spheroidal Functions]]<br>
-! scope="col" style="position: sticky; top: 0;" | DLMF
+; Applications : [[30.13|30.13 Wave Equation in Prolate Spheroidal Coordinates]]<br>[[30.14|30.14 Wave Equation in Oblate Spheroidal Coordinates]]<br>[[30.15|30.15 Signal Analysis]]<br>
-! scope="col" style="position: sticky; top: 0;" | Formula
+; Computation : [[30.16|30.16 Methods of Computation]]<br>[[30.17|30.17 Tables]]<br>[[30.18|30.18 Software]]<br>
-! scope="col" style="position: sticky; top: 0;" | Constraints
-! scope="col" style="position: sticky; top: 0;" | Maple
-! scope="col" style="position: sticky; top: 0;" | Mathematica
-! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
-! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
-! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
-! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
-|-
-| [https://dlmf.nist.gov/30.1#Ex3 30.1#Ex3] || [[Item:Q8817|<math>S^{(1)}_{mn}(\gamma,0) = (-1)^{m}\FerrersP[m]{n}@{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>S^{(1)}_{mn}(\gamma,0) = (-1)^{m}\FerrersP[m]{n}@{0}</syntaxhighlight> || <math>|(\tfrac{1}{2}-\tfrac{1}{2}0)| < 1</math> || <syntaxhighlight lang=mathematica>(S[m, n])^(1)(gamma , 0) = (- 1)^(m)* LegendreP(n, m, 0)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[S, m, n])^(1)[\[Gamma], 0] == (- 1)^(m)* LegendreP[n, m, 0]</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/30.2.E1 30.2.E1] || [[Item:Q8819|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 - (z)^(2))*diff(w, z))+(lambda + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))*w, z) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ \[Gamma]^(2)*(1 - (z)^(2))-Divide[\[Mu]^(2),1 - (z)^(2)])*w, z] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [260 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6668220767+1.154969718*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.154431362-.6665112581*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.0, 2.220446049250313*^-16]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.220446049250313*^-16, -3.4641016151377553]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.2.E2 30.2.E2] || [[Item:Q8820|<math>\deriv[2]{g}{t}+\left(\lambda+\frac{1}{4}+\gamma^{2}\sin^{2}@@{t}-\frac{\mu^{2}-\frac{1}{4}}{\sin^{2}@@{t}}\right)g = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{g}{t}+\left(\lambda+\frac{1}{4}+\gamma^{2}\sin^{2}@@{t}-\frac{\mu^{2}-\frac{1}{4}}{\sin^{2}@@{t}}\right)g = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(g, [t$(2)])+(lambda +(1)/(4)+ (gamma)^(2)* (sin(t))^(2)-((mu)^(2)-(1)/(4))/((sin(t))^(2)))*g = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[g, {t, 2}]+(\[Lambda]+Divide[1,4]+ \[Gamma]^(2)* (Sin[t])^(2)-Divide[\[Mu]^(2)-Divide[1,4],(Sin[t])^(2)])*g == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.221198255+.2773804949*I
-Test Values: {g = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.221198255+.2773804949*I
-Test Values: {g = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9341014939589334, 1.1066213513350005]
-Test Values: {Rule[g, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.9341014939589334, 3.116679181619939]
-Test Values: {Rule[g, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.2#Ex1 30.2#Ex1] || [[Item:Q8821|<math>z = \cos@@{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \cos@@{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = cos(t)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Cos[t]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7952882023+.5000000000*I
-Test Values: {t = -3/2, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5707372017+.8660254040*I
-Test Values: {t = -3/2, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [42 / 42]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7952882021167358, 0.49999999999999994]
-Test Values: {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.5707372016677027, 0.8660254037844387]
-Test Values: {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.2.E4 30.2.E4] || [[Item:Q8823|<math>(\zeta^{2}-\gamma^{2})\deriv[2]{w}{\zeta}+2\zeta\deriv{w}{\zeta}+\left(\zeta^{2}-\lambda-\gamma^{2}-\frac{\gamma^{2}\mu^{2}}{\zeta^{2}-\gamma^{2}}\right)w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\zeta^{2}-\gamma^{2})\deriv[2]{w}{\zeta}+2\zeta\deriv{w}{\zeta}+\left(\zeta^{2}-\lambda-\gamma^{2}-\frac{\gamma^{2}\mu^{2}}{\zeta^{2}-\gamma^{2}}\right)w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((zeta)^(2)- (gamma)^(2))*diff(w, [zeta$(2)])+ 2*zeta*diff(w, zeta)+((zeta)^(2)- lambda - (gamma)^(2)-((gamma)^(2)* (mu)^(2))/((zeta)^(2)- (gamma)^(2)))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(\[Zeta]^(2)- \[Gamma]^(2))*D[w, {\[Zeta], 2}]+ 2*\[Zeta]*D[w, \[Zeta]]+(\[Zeta]^(2)- \[Lambda]- \[Gamma]^(2)-Divide[\[Gamma]^(2)* \[Mu]^(2),\[Zeta]^(2)- \[Gamma]^(2)])*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.159496529-.1040714462*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5887458836-1.840397716*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex4 30.3#Ex4] || [[Item:Q8832|<math>\alpha_{k} = \gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{k} = \gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[k] = (gamma)^(2)*((k + 2*m + 1)*(k + 2*m + 2))/((2*k + 2*m + 3)*(2*k + 2*m + 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], k] == \[Gamma]^(2)*Divide[(k + 2*m + 1)*(k + 2*m + 2),(2*k + 2*m + 3)*(2*k + 2*m + 5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex5 30.3#Ex5] || [[Item:Q8833|<math>\beta_{k} = (k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k+2m+3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{k} = (k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k+2m+3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[k] = (k + m)*(k + m + 1)- 2*(gamma)^(2)*((k + m)*(k + m + 1)- 1 + (m)^(2))/((2*k + 2*m - 1)*(2*k + 2*m + 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], k] == (k + m)*(k + m + 1)- 2*\[Gamma]^(2)*Divide[(k + m)*(k + m + 1)- 1 + (m)^(2),(2*k + 2*m - 1)*(2*k + 2*m + 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex6 30.3#Ex6] || [[Item:Q8834|<math>\gamma_{k} = \gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{k} = \gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((gamma)^(2)) = (gamma)^(2)*((k - 1)*k)/((2*k + 2*m - 3)*(2*k + 2*m - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(\[Gamma]^(2)) == \[Gamma]^(2)*Divide[(k - 1)*k,(2*k + 2*m - 3)*(2*k + 2*m - 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex7 30.3#Ex7] || [[Item:Q8836|<math>\ell_{0} = n(n+1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell_{0} = n(n+1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell[0] = n*(n + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[ScriptL], 0] == n*(n + 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex8 30.3#Ex8] || [[Item:Q8837|<math>2\ell_{2} = -1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2\ell_{2} = -1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*ell[2] = - 1 -((2*m - 1)*(2*m + 1))/((2*n - 1)*(2*n + 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[\[ScriptL], 2] == - 1 -Divide[(2*m - 1)*(2*m + 1),(2*n - 1)*(2*n + 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3#Ex9 30.3#Ex9] || [[Item:Q8838|<math>2\ell_{4} = \frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2\ell_{4} = \frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*ell[4] = ((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 3)*(2*n - 1)^(3)*(2*n + 1))-((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n + 1)*(2*n + 3)^(3)*(2*n + 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[\[ScriptL], 4] == Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 3)*(2*n - 1)^(3)*(2*n + 1)]-Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n + 1)*(2*n + 3)^(3)*(2*n + 5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3.E10 30.3.E10] || [[Item:Q8839|<math>\ell_{6} = (4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell_{6} = (4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell[6] = (4*(m)^(2)- 1)*(((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7))-((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[ScriptL], 6] == (4*(m)^(2)- 1)*(Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7)]-Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3)])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.3.E11 30.3.E11] || [[Item:Q8840|<math>\ell_{8} = 2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell_{8} = 2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell[8] = 2*(4*(m)^(2)- 1)^(2)* A +(1)/(16)*B +(1)/(8)*C +(1)/(2)*(((n - m - 1)*(n - m)*(n - m + 1)*(n - m + 2)*(n + m - 1)*(n + m)*(n + m + 1)*(n + m + 2))/((2*n - 3)*(2*n - 1)^(4)*(2*n + 1)^(2)*(2*n + 3)^(4)*(2*n + 5)))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[ScriptL], 8] == 2*(4*(m)^(2)- 1)^(2)* A +Divide[1,16]*B +Divide[1,8]*C +Divide[1,2]*(Divide[(n - m - 1)*(n - m)*(n - m + 1)*(n - m + 2)*(n + m - 1)*(n + m)*(n + m + 1)*(n + m + 2),(2*n - 3)*(2*n - 1)^(4)*(2*n + 1)^(2)*(2*n + 3)^(4)*(2*n + 5)])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex5 30.9#Ex5] || [[Item:Q8883|<math>2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(16)* beta[4] = - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(16)* Subscript[\[Beta], 4] == - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex6 30.9#Ex6] || [[Item:Q8884|<math>2^{20}\beta_{5} = -527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{20}\beta_{5} = -527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(20)* beta[5] = - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(20)* Subscript[\[Beta], 5] == - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex7 30.9#Ex7] || [[Item:Q8886|<math>2c_{0} = -q^{2}-1+m^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2c_{0} = -q^{2}-1+m^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*c[0] = - (q)^(2)- 1 + (m)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">2*Subscript[c, 0] == - (q)^(2)- 1 + (m)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex8 30.9#Ex8] || [[Item:Q8887|<math>8c_{1} = -q^{3}-q+m^{2}q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>8c_{1} = -q^{3}-q+m^{2}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*c[1] = - (q)^(3)- q + (m)^(2)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">8*Subscript[c, 1] == - (q)^(3)- q + (m)^(2)* q</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex9 30.9#Ex9] || [[Item:Q8888|<math>2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(6)* c[2] = - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(6)* Subscript[c, 2] == - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex10 30.9#Ex10] || [[Item:Q8889|<math>2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(9)* c[3] = - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(9)* Subscript[c, 3] == - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex11 30.9#Ex11] || [[Item:Q8890|<math>2^{10}c_{4} = -63q^{6}-340q^{4}-239q^{2}-14+10m^{2}(10q^{4}+23q^{2}+3)-3m^{4}(13q^{2}+6)+2m^{6}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{10}c_{4} = -63q^{6}-340q^{4}-239q^{2}-14+10m^{2}(10q^{4}+23q^{2}+3)-3m^{4}(13q^{2}+6)+2m^{6}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(10)* c[4] = - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(10)* Subscript[c, 4] == - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.9#Ex12 30.9#Ex12] || [[Item:Q8891|<math>2^{13}c_{5} = -527q^{7}-4139q^{5}-5221q^{3}-1009q+m^{2}(939q^{5}+3750q^{3}+1591q)-m^{4}(465q^{3}+635q)+53m^{6}q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>2^{13}c_{5} = -527q^{7}-4139q^{5}-5221q^{3}-1009q+m^{2}(939q^{5}+3750q^{3}+1591q)-m^{4}(465q^{3}+635q)+53m^{6}q</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(13)* c[5] = - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(2)^(13)* Subscript[c, 5] == - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/30.11#Ex5 30.11#Ex5] || [[Item:Q8899|<math>\radsphwaveS{m}{3}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}+\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\radsphwaveS{m}{3}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}+\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SpheroidalS3[n, m, z, \[Gamma]] == SpheroidalS1[n, m, z, \[Gamma]]+ I*SpheroidalS2[n, m, z, \[Gamma]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/30.11#Ex6 30.11#Ex6] || [[Item:Q8900|<math>\radsphwaveS{m}{4}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}-\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\radsphwaveS{m}{4}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}-\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SpheroidalS4[n, m, z, \[Gamma]] == SpheroidalS1[n, m, z, \[Gamma]]- I*SpheroidalS2[n, m, z, \[Gamma]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/30.11.E7 30.11.E7] || [[Item:Q8902|<math>\Wronskian@{\radsphwaveS{m}{1}{n}@{z}{\gamma},\radsphwaveS{m}{2}{n}@{z}{\gamma}} = \frac{1}{\gamma(z^{2}-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wronskian@{\radsphwaveS{m}{1}{n}@{z}{\gamma},\radsphwaveS{m}{2}{n}@{z}{\gamma}} = \frac{1}{\gamma(z^{2}-1)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Wronskian[{SpheroidalS1[n, m, z, \[Gamma]], SpheroidalS2[n, m, z, \[Gamma]]}, z] == Divide[1,\[Gamma]*((z)^(2)- 1)]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/30.12.E1 30.12.E1] || [[Item:Q8908|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+{\left(\lambda+\alpha z+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+{\left(\lambda+\alpha z+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 - (z)^(2))*diff(w, z))+(lambda + alpha*z + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))*w, z) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ \[Alpha]*z + \[Gamma]^(2)*(1 - (z)^(2))-Divide[\[Mu]^(2),1 - (z)^(2)])*w, z] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.965860183+1.904969718*I
-Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.453469468+.8348874183e-1*I
-Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.299038105676658, 0.7500000000000002]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.2990381056766578, -2.7141016151377553]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.12.E2 30.12.E2] || [[Item:Q8909|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\alpha(\alpha+1)}{z^{2}}-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\alpha(\alpha+1)}{z^{2}}-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 - (z)^(2))*diff(w, z))+(lambda + (gamma)^(2)*(1 - (z)^(2))-(alpha*(alpha + 1))/((z)^(2))-((mu)^(2))/(1 - (z)^(2)))*w, z) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ \[Gamma]^(2)*(1 - (z)^(2))-Divide[\[Alpha]*(\[Alpha]+ 1),(z)^(2)]-Divide[\[Mu]^(2),1 - (z)^(2)])*w, z] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.416822075-5.340220804*I
-Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 7.649621884+3.083488740*I
-Test Values: {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[5.749999999999999, -6.495190528383291]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.749999999999999, -9.959292143521045]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.13#Ex4 30.13#Ex4] || [[Item:Q8913|<math>1 < \xi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>1 < \xi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">1 < xi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">1 < \[Xi]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.13#Ex5 30.13#Ex5] || [[Item:Q8914|<math>-1 < \eta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>-1 < \eta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 1 < eta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 1 < \[Eta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.13#Ex6 30.13#Ex6] || [[Item:Q8915|<math>0 \leq \phi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 \leq \phi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= phi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= \[Phi]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/30.13.E3 30.13.E3] || [[Item:Q8916|<math>h_{\xi}^{2} = \left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>h_{\xi}^{2} = \left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(h[xi])^(2) = (diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(x + y*I, xi))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[h, \[Xi]])^(2) == (D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[x + y*I, \[Xi]])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
-Test Values: {x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2, h[xi] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5000000004-.8660254040*I
-Test Values: {x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2, h[xi] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5000000000000001, 0.8660254037844386]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ξ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.4999999999999998, -0.8660254037844387]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ξ], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E3 30.13.E3] || [[Item:Q8916|<math>\left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{\xi^{2}-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{\xi^{2}-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(x + y*I, xi))^(2) = ((c)^(2)*((xi)^(2)- (eta)^(2)))/((xi)^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[x + y*I, \[Xi]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)- \[Eta]^(2)),\[Xi]^(2)- 1]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.250000002-1.299038105*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.250000002-1.299038105*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.25, -1.2990381056766578]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.25, -1.2990381056766578]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E4 30.13.E4] || [[Item:Q8917|<math>h_{\eta}^{2} = \left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>h_{\eta}^{2} = \left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(h[eta])^(2) = (diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(x + y*I, eta))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[h, \[Eta]])^(2) == (D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[x + y*I, \[Eta]])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[eta] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5000000004-.8660254040*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[eta] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5000000000000001, 0.8660254037844386]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, η], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.4999999999999998, -0.8660254037844387]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, η], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E4 30.13.E4] || [[Item:Q8917|<math>\left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{1-\eta^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{1-\eta^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(x + y*I, eta))^(2) = ((c)^(2)*((xi)^(2)- (eta)^(2)))/(1 - (eta)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[x + y*I, \[Eta]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)- \[Eta]^(2)),1 - \[Eta]^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.250000002+3.897114318*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.250000002+3.897114318*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.2500000000000004, 3.897114317029973]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.2500000000000004, 3.897114317029973]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E5 30.13.E5] || [[Item:Q8918|<math>h_{\phi}^{2} = \left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>h_{\phi}^{2} = \left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(h[phi])^(2) = (diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(x + y*I, phi))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[h, \[Phi]])^(2) == (D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[x + y*I, \[Phi]])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[phi] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5000000004-.8660254040*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[phi] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5000000000000001, 0.8660254037844386]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ϕ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.4999999999999998, -0.8660254037844387]
-Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ϕ], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E5 30.13.E5] || [[Item:Q8918|<math>\left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2} = c^{2}(\xi^{2}-1)(1-\eta^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2} = c^{2}(\xi^{2}-1)(1-\eta^{2})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(x + y*I, phi))^(2) = (c)^(2)*((xi)^(2)- 1)*(1 - (eta)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[x + y*I, \[Phi]])^(2) == (c)^(2)*(\[Xi]^(2)- 1)*(1 - \[Eta]^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.125000002-1.948557157*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.125000002-1.948557157*I
-Test Values: {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.125, -1.9485571585149866]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.125, -1.9485571585149866]
-Test Values: {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E6 30.13.E6] || [[Item:Q8919|<math>\frac{1}{h_{\xi}h_{\eta}h_{\phi}}\left(\pderiv{}{\xi}\left(\frac{h_{\eta}h_{\phi}}{h_{\xi}}\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left(\frac{h_{\xi}h_{\phi}}{h_{\eta}}\pderiv{}{\eta}\right)+\pderiv{}{\phi}\left(\frac{h_{\xi}h_{\eta}}{h_{\phi}}\pderiv{}{\phi}\right)\right) = \frac{1}{c^{2}(\xi^{2}-\eta^{2})}\left(\pderiv{}{\xi}\left((\xi^{2}-1)\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left((1-\eta^{2})\pderiv{}{\eta}\right)+\frac{\xi^{2}-\eta^{2}}{(\xi^{2}-1)(1-\eta^{2})}\pderiv[2]{}{\phi}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{h_{\xi}h_{\eta}h_{\phi}}\left(\pderiv{}{\xi}\left(\frac{h_{\eta}h_{\phi}}{h_{\xi}}\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left(\frac{h_{\xi}h_{\phi}}{h_{\eta}}\pderiv{}{\eta}\right)+\pderiv{}{\phi}\left(\frac{h_{\xi}h_{\eta}}{h_{\phi}}\pderiv{}{\phi}\right)\right) = \frac{1}{c^{2}(\xi^{2}-\eta^{2})}\left(\pderiv{}{\xi}\left((\xi^{2}-1)\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left((1-\eta^{2})\pderiv{}{\eta}\right)+\frac{\xi^{2}-\eta^{2}}{(\xi^{2}-1)(1-\eta^{2})}\pderiv[2]{}{\phi}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(diff((((xi)^(2)- 1)*diff((1)/((c)^(2)*((xi)^(2)- (eta)^(2)))*((xi)^(2)- 1), xi))+ diff(diff(((1 - (eta)^(2))*diff((diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ diff(((h[xi]*h[phi])/(h[eta])*diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ (h[xi]*h[phi])/(h[eta]), eta))+ diff((h[xi]*h[eta])/(h[phi])*diff(((h[xi]*h[phi])/(h[eta])*diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ (h[xi]*h[phi])/(h[eta]), eta))+ (h[xi]*h[eta])/(h[phi]), phi), phi), eta), xi)) (((xi)^(2)- 1)*diff((1)/((c)^(2)*((xi)^(2)- (eta)^(2)))*((xi)^(2)- 1), xi))+ (1 - (eta)^(2)), eta))+((xi)^(2)- (eta)^(2))/(((xi)^(2)- 1)*(1 - (eta)^(2))), [phi$(2)]), eta), xi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[((\[Xi]^(2)- 1)*D[Divide[1,(c)^(2)*(\[Xi]^(2)- \[Eta]^(2))]*(\[Xi]^(2)- 1), \[Xi]])+ D[D[((1 - \[Eta]^(2))*D[(D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ D[(Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]]*D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]], \[Eta]])+ D[Divide[Subscript[h, \[Xi]]*Subscript[h, \[Eta]],Subscript[h, \[Phi]]]*D[(Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]]*D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]], \[Eta]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Eta]],Subscript[h, \[Phi]]], \[Phi]], \[Phi]], \[Eta]], \[Xi]]) ((\[Xi]^(2)- 1)*D[Divide[1,(c)^(2)*(\[Xi]^(2)- \[Eta]^(2))]*(\[Xi]^(2)- 1), \[Xi]])+ (1 - \[Eta]^(2)), \[Eta]])+Divide[\[Xi]^(2)- \[Eta]^(2),(\[Xi]^(2)- 1)*(1 - \[Eta]^(2))], {\[Phi], 2}], \[Eta]], \[Xi]])</syntaxhighlight> || Translation Error || Translation Error || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.13.E8 30.13.E8] || [[Item:Q8921|<math>w(\xi,\eta,\phi) = w_{1}(\xi)w_{2}(\eta)w_{3}(\phi)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(\xi,\eta,\phi) = w_{1}(\xi)w_{2}(\eta)w_{3}(\phi)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(xi , eta , phi) = w[1](xi)* w[2](eta)* w[3](phi)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[\[Xi], \[Eta], \[Phi]] == Subscript[w, 1][\[Xi]]* Subscript[w, 2][\[Eta]]* Subscript[w, 3][\[Phi]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/30.13.E9 30.13.E9] || [[Item:Q8922|<math>\deriv{}{\xi}\left((1-\xi^{2})\deriv{w_{1}}{\xi}\right)+\left(\lambda+\gamma^{2}(1-\xi^{2})-\frac{\mu^{2}}{1-\xi^{2}}\right)w_{1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{\xi}\left((1-\xi^{2})\deriv{w_{1}}{\xi}\right)+\left(\lambda+\gamma^{2}(1-\xi^{2})-\frac{\mu^{2}}{1-\xi^{2}}\right)w_{1} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 - (xi)^(2))*diff(w[1], xi))+(lambda + (gamma)^(2)*(1 - (xi)^(2))-((mu)^(2))/(1 - (xi)^(2)))*w[1], xi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 - \[Xi]^(2))*D[Subscript[w, 1], \[Xi]])+(\[Lambda]+ \[Gamma]^(2)*(1 - \[Xi]^(2))-Divide[\[Mu]^(2),1 - \[Xi]^(2)])*Subscript[w, 1], \[Xi]] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [260 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6668220767+1.154969718*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.154969718+.6668220767*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.0, 2.220446049250313*^-16]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 1.9999999999999998]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E10 30.13.E10] || [[Item:Q8923|<math>\deriv{}{\eta}\left((1-\eta^{2})\deriv{w_{2}}{\eta}\right)+\left(\lambda+\gamma^{2}(1-\eta^{2})-\frac{\mu^{2}}{1-\eta^{2}}\right)w_{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{\eta}\left((1-\eta^{2})\deriv{w_{2}}{\eta}\right)+\left(\lambda+\gamma^{2}(1-\eta^{2})-\frac{\mu^{2}}{1-\eta^{2}}\right)w_{2} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 - (eta)^(2))*diff(w[2], eta))+(lambda + (gamma)^(2)*(1 - (eta)^(2))-((mu)^(2))/(1 - (eta)^(2)))*w[2], eta) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 - \[Eta]^(2))*D[Subscript[w, 2], \[Eta]])+(\[Lambda]+ \[Gamma]^(2)*(1 - \[Eta]^(2))-Divide[\[Mu]^(2),1 - \[Eta]^(2)])*Subscript[w, 2], \[Eta]] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6668220767+1.154969718*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.154969718+.6668220767*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w[2] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.0, 2.220446049250313*^-16]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.0, 1.9999999999999998]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E11 30.13.E11] || [[Item:Q8924|<math>\deriv[2]{w_{3}}{\phi}+\mu^{2}w_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w_{3}}{\phi}+\mu^{2}w_{3} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w[3], [phi$(2)])+ (mu)^(2)* w[3] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[w, 3], {\[Phi], 2}]+ \[Mu]^(2)* Subscript[w, 3] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3233738859e-9+1.000000001*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.000000001+.3464101616e-9*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, w[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 1.0]
-Test Values: {Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.0
-Test Values: {Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E12 30.13.E12] || [[Item:Q8925|<math>w_{3}(\phi) = a_{3}\cos@{m\phi}+b_{3}\sin@{m\phi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{3}(\phi) = a_{3}\cos@{m\phi}+b_{3}\sin@{m\phi}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[3](phi) = a[3]*cos(m*phi)+ b[3]*sin(m*phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 3][\[Phi]] == Subscript[a, 3]*Cos[m*\[Phi]]+ Subscript[b, 3]*Sin[m*\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9062441475+.1226650086*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, a[3] = 1/2*3^(1/2)+1/2*I, b[3] = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.278771435+1.396327873*I
-Test Values: {phi = 1/2*3^(1/2)+1/2*I, a[3] = 1/2*3^(1/2)+1/2*I, b[3] = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.9062441474191866, 0.12266500824612203]
-Test Values: {Rule[m, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.2787714355239146, 1.3963278722366796]
-Test Values: {Rule[m, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.13.E14 30.13.E14] || [[Item:Q8927|<math>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{\xi}{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{\xi}{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 1][\[Xi]] == Subscript[a, 1]*SpheroidalS1[n, m, \[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, \[Xi], \[Gamma]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/30.13.E15 30.13.E15] || [[Item:Q8928|<math>\radsphwaveS{m}{1}{n}@{\xi_{0}}{\gamma} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\radsphwaveS{m}{1}{n}@{\xi_{0}}{\gamma} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SpheroidalS1[n, m, Subscript[\[Xi], 0], \[Gamma]] == 0</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.13.E16 30.13.E16] || [[Item:Q8929|<math>w_{1}(\xi_{1}) = w_{1}(\xi_{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w_{1}(\xi_{1}) = w_{1}(\xi_{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[1](xi[1]) = w[1](xi[2])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[w, 1][Subscript[\[Xi], 1]] == Subscript[w, 1][Subscript[\[Xi], 2]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14#Ex4 30.14#Ex4] || [[Item:Q8933|<math>0 < \xi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < \xi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < xi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < \[Xi]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14#Ex5 30.14#Ex5] || [[Item:Q8934|<math>-1 < \eta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>-1 < \eta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 1 < eta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">- 1 < \[Eta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14#Ex6 30.14#Ex6] || [[Item:Q8935|<math>0 \leq \phi</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 \leq \phi</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= phi</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= \[Phi]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14.E3 30.14.E3] || [[Item:Q8936|<math>h_{\xi}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1+\xi^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h_{\xi}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1+\xi^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(h[xi])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 + (xi)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[h, \[Xi]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 + \[Xi]^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14.E4 30.14.E4] || [[Item:Q8937|<math>h_{\eta}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1-\eta^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h_{\eta}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1-\eta^{2}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(h[eta])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 - (eta)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[h, \[Eta]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 - \[Eta]^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.14.E5 30.14.E5] || [[Item:Q8938|<math>h_{\phi}^{2} = c^{2}(\xi^{2}+1)(1-\eta^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h_{\phi}^{2} = c^{2}(\xi^{2}+1)(1-\eta^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(h[phi])^(2) = (c)^(2)*((xi)^(2)+ 1)*(1 - (eta)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[h, \[Phi]])^(2) == (c)^(2)*(\[Xi]^(2)+ 1)*(1 - \[Eta]^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/30.14.E7 30.14.E7] || [[Item:Q8940|<math>\deriv{}{\xi}\left((1+\xi^{2})\deriv{w_{1}}{\xi}\right)-\left(\lambda+\gamma^{2}(1+\xi^{2})-\frac{\mu^{2}}{1+\xi^{2}}\right)w_{1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{\xi}\left((1+\xi^{2})\deriv{w_{1}}{\xi}\right)-\left(\lambda+\gamma^{2}(1+\xi^{2})-\frac{\mu^{2}}{1+\xi^{2}}\right)w_{1} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((1 + (xi)^(2))*diff(w[1], xi))-(lambda + (gamma)^(2)*(1 + (xi)^(2))-((mu)^(2))/(1 + (xi)^(2)))*w[1], xi) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((1 + \[Xi]^(2))*D[Subscript[w, 1], \[Xi]])-(\[Lambda]+ \[Gamma]^(2)*(1 + \[Xi]^(2))-Divide[\[Mu]^(2),1 + \[Xi]^(2)])*Subscript[w, 1], \[Xi]] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [260 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6665112581-1.154431362*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.154431362-.6665112581*I
-Test Values: {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6666666666666664, -2.309401076758503]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.309401076758503, 0.6666666666666662]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.14.E8 30.14.E8] || [[Item:Q8941|<math>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{i\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{i\xi}{\gamma}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{i\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{i\xi}{\gamma}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 1][\[Xi]] == Subscript[a, 1]*SpheroidalS1[n, m, I*\[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, I*\[Xi], \[Gamma]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/30.14.E9 30.14.E9] || [[Item:Q8942|<math>\radsphwaveS{m}{1}{n}@{\iunit\xi_{0}}{\gamma} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\radsphwaveS{m}{1}{n}@{\iunit\xi_{0}}{\gamma} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SpheroidalS1[n, m, I*Subscript[\[Xi], 0], \[Gamma]] == 0</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.30414296182717676, -0.005578569442222112]
-Test Values: {Rule[j, 4], Rule[m, 1], Rule[n, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.05539464168732451, -0.030004541724887247]
-Test Values: {Rule[j, 4], Rule[m, 1], Rule[n, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/30.15.E11 30.15.E11] || [[Item:Q8954|<math>\acos@@{\sqrt{\mathrm{B}}}+\acos@@{\sqrt{\alpha}} = \acos@@{\sqrt{\Lambda_{0}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\acos@@{\sqrt{\mathrm{B}}}+\acos@@{\sqrt{\alpha}} = \acos@@{\sqrt{\Lambda_{0}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>arccos(sqrt(B))+ arccos(sqrt(alpha)) = arccos(sqrt(Lambda[0]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcCos[Sqrt[B]]+ ArcCos[Sqrt[\[Alpha]]] == ArcCos[Sqrt[Subscript[\[CapitalLambda], 0]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6584789493*I
-Test Values: {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6623382543+1.000904144*I
-Test Values: {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, 0.6584789484624083]
-Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.6623382542357523, 1.0009041434383552]
-Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.15.E12 30.15.E12] || [[Item:Q8955|<math>\mathrm{B} = \left(\sqrt{\Lambda_{0}\alpha}+\sqrt{1-\Lambda_{0}}\sqrt{1-\alpha}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\mathrm{B} = \left(\sqrt{\Lambda_{0}\alpha}+\sqrt{1-\Lambda_{0}}\sqrt{1-\alpha}\right)^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B = (sqrt(Lambda[0]*alpha)+sqrt(1 - Lambda[0])*sqrt(1 - alpha))^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B == (Sqrt[Subscript[\[CapitalLambda], 0]*\[Alpha]]+Sqrt[1 - Subscript[\[CapitalLambda], 0]]*Sqrt[1 - \[Alpha]])^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.15#Ex4 30.15#Ex4] || [[Item:Q8957|<math>a = \sqrt{\frac{\alpha}{\Lambda_{0}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a = \sqrt{\frac{\alpha}{\Lambda_{0}}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a = sqrt((alpha)/(Lambda[0]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a == Sqrt[Divide[\[Alpha],Subscript[\[CapitalLambda], 0]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.15#Ex5 30.15#Ex5] || [[Item:Q8958|<math>b = \sqrt{\frac{1-\alpha}{1-\Lambda_{0}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b = \sqrt{\frac{1-\alpha}{1-\Lambda_{0}}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b = sqrt((1 - alpha)/(1 - Lambda[0]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b == Sqrt[Divide[1 - \[Alpha],1 - Subscript[\[CapitalLambda], 0]]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex1 30.16#Ex1] || [[Item:Q8959|<math>A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 2)*(m + 2*j - 1)- 2*(gamma)^(2)*((m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2))/((2*m + 4*j - 5)*(2*m + 4*j - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 2)*(m + 2*j - 1)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2),(2*m + 4*j - 5)*(2*m + 4*j - 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex2 30.16#Ex2] || [[Item:Q8960|<math>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j - 1)*(2*m + 2*j))/((2*m + 4*j - 1)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j - 1)*(2*m + 2*j),(2*m + 4*j - 1)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex3 30.16#Ex3] || [[Item:Q8961|<math>A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 3)*(2*j - 2))/((2*m + 4*j - 7)*(2*m + 4*j - 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 3)*(2*j - 2),(2*m + 4*j - 7)*(2*m + 4*j - 5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16.E2 30.16.E2] || [[Item:Q8962|<math>\alpha_{j,d+1} \leq \alpha_{j,d}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{j,d+1} \leq \alpha_{j,d}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[j , d + 1] <= alpha[j , d]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], j , d + 1] <= Subscript[\[Alpha], j , d]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex4 30.16#Ex4] || [[Item:Q8965|<math>\alpha_{2,2} = 14.18833\;246</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,2} = 14.18833\;246</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 2] = 14.18833246</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 2] == 14.18833246</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex5 30.16#Ex5] || [[Item:Q8966|<math>\alpha_{2,3} = 13.98002\;013</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,3} = 13.98002\;013</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 3] = 13.98002013</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 3] == 13.98002013</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex6 30.16#Ex6] || [[Item:Q8967|<math>\alpha_{2,4} = 13.97907\;459</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,4} = 13.97907\;459</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 4] = 13.97907459</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 4] == 13.97907459</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex7 30.16#Ex7] || [[Item:Q8968|<math>\alpha_{2,5} = 13.97907\;345</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,5} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 5] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 5] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex8 30.16#Ex8] || [[Item:Q8969|<math>\alpha_{2,6} = 13.97907\;345</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,6} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 6] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 6] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex9 30.16#Ex9] || [[Item:Q8970|<math>A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 1)*(m + 2*j)- 2*(gamma)^(2)*((m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2))/((2*m + 4*j - 3)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 1)*(m + 2*j)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2),(2*m + 4*j - 3)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex10 30.16#Ex10] || [[Item:Q8971|<math>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j)*(2*m + 2*j + 1))/((2*m + 4*j + 1)*(2*m + 4*j + 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j)*(2*m + 2*j + 1),(2*m + 4*j + 1)*(2*m + 4*j + 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex11 30.16#Ex11] || [[Item:Q8972|<math>A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 2)*(2*j - 1))/((2*m + 4*j - 5)*(2*m + 4*j - 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 2)*(2*j - 1),(2*m + 4*j - 5)*(2*m + 4*j - 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16.E7 30.16.E7] || [[Item:Q8973|<math>\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((exp(1)[j , d])^(2)*(factorial(n + m + 2*j - 2*p))/(factorial(n - m + 2*j - 2*p))*(1)/(2*n + 4*j - 4*p + 1), j = 1..d) = (factorial(n + m))/(factorial(n - m))*(1)/(2*n + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[E, j , d])^(2)*Divide[(n + m + 2*j - 2*p)!,(n - m + 2*j - 2*p)!]*Divide[1,2*n + 4*j - 4*p + 1], {j, 1, d}, GenerateConditions->None] == Divide[(n + m)!,(n - m)!]*Divide[1,2*n + 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|}
 </div>

Results of Spheroidal Wave Functions: Difference between revisions

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