Results of Lamé Functions: Difference between revisions

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Notation: 29.1 Special Notation
Lamé Functions: 29.2 Differential Equations
29.3 Definitions and Basic Properties
29.4 Graphics
29.5 Special Cases and Limiting Forms
29.6 Fourier Series
29.7 Asymptotic Expansions
29.8 Integral Equations
29.9 Stability
29.10 Lamé Functions with Imaginary Periods
29.11 Lamé Wave Equation
Lamé Polynomials: 29.12 Definitions
29.13 Graphics
29.14 Orthogonality
29.15 Fourier Series and Chebyshev Series
29.16 Asymptotic Expansions
29.17 Other Solutions
Applications: 29.18 Mathematical Applications
29.19 Physical Applications
Computation: 29.20 Methods of Computation
29.21 Tables
29.22 Software

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-<div style="width: 100%; height: 75vh; overflow: auto;">
+<div style="-moz-column-count:2; column-count:2;">
-{| class="wikitable sortable" style="margin: 0;"
+; Notation : [[29.1|29.1 Special Notation]]<br>
-|-
+; Lamé Functions : [[29.2|29.2 Differential Equations]]<br>[[29.3|29.3 Definitions and Basic Properties]]<br>[[29.4|29.4 Graphics]]<br>[[29.5|29.5 Special Cases and Limiting Forms]]<br>[[29.6|29.6 Fourier Series]]<br>[[29.7|29.7 Asymptotic Expansions]]<br>[[29.8|29.8 Integral Equations]]<br>[[29.9|29.9 Stability]]<br>[[29.10|29.10 Lamé Functions with Imaginary Periods]]<br>[[29.11|29.11 Lamé Wave Equation]]<br>
-! scope="col" style="position: sticky; top: 0;" | DLMF
+; Lamé Polynomials : [[29.12|29.12 Definitions]]<br>[[29.13|29.13 Graphics]]<br>[[29.14|29.14 Orthogonality]]<br>[[29.15|29.15 Fourier Series and Chebyshev Series]]<br>[[29.16|29.16 Asymptotic Expansions]]<br>[[29.17|29.17 Other Solutions]]<br>
-! scope="col" style="position: sticky; top: 0;" | Formula
+; Applications : [[29.18|29.18 Mathematical Applications]]<br>[[29.19|29.19 Physical Applications]]<br>
-! scope="col" style="position: sticky; top: 0;" | Constraints
+; Computation : [[29.20|29.20 Methods of Computation]]<br>[[29.21|29.21 Tables]]<br>[[29.22|29.22 Software]]<br>
-! 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/29.2.E1 29.2.E1] || [[Item:Q8574|<math>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k})w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k})w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(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: .9359870183-.3879581426*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5826053060-2.538844794*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9359870178672973, -0.3879581414973573]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.5826053037338313, -2.538844793552361]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.2.E2 29.2.E2] || [[Item:Q8575|<math>\deriv[2]{w}{\xi}+\frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)\deriv{w}{\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi-k^{-2})}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{\xi}+\frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)\deriv{w}{\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi-k^{-2})}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=((JacobiSN(z, k))^(2)), diff( w, temp$(2) ) )+(1)/(2)*((1)/((JacobiSN(z, k))^(2))+(1)/(((JacobiSN(z, k))^(2))- 1)+(1)/(((JacobiSN(z, k))^(2))- (k)^(- 2)))*subs( temp=((JacobiSN(z, k))^(2)), diff( w, temp$(1) ) )+(h*(k)^(- 2)- nu*(nu + 1)*((JacobiSN(z, k))^(2)))/(4*((JacobiSN(z, k))^(2))*(((JacobiSN(z, k))^(2))- 1)*(((JacobiSN(z, k))^(2))- (k)^(- 2)))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[w, {temp, 2}]/.temp-> ((JacobiSN[z, (k)^2])^(2)))+Divide[1,2]*(Divide[1,(JacobiSN[z, (k)^2])^(2)]+Divide[1,((JacobiSN[z, (k)^2])^(2))- 1]+Divide[1,((JacobiSN[z, (k)^2])^(2))- (k)^(- 2)])*(D[w, {temp, 1}]/.temp-> ((JacobiSN[z, (k)^2])^(2)))+Divide[h*(k)^(- 2)- \[Nu]*(\[Nu]+ 1)*((JacobiSN[z, (k)^2])^(2)),4*((JacobiSN[z, (k)^2])^(2))*(((JacobiSN[z, (k)^2])^(2))- 1)*(((JacobiSN[z, (k)^2])^(2))- (k)^(- 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: .9804044245+.4985385652*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3643094905+3.048781532*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9804044230224559, 0.49853856488927895]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.36430949083593944, 3.048781532678858]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.2.E4 29.2.E4] || [[Item:Q8577|<math>(1-k^{2}\cos^{2}@@{\phi})\deriv[2]{w}{\phi}+k^{2}\cos@@{\phi}\sin@@{\phi}\deriv{w}{\phi}+(h-\nu(\nu+1)k^{2}\cos^{2}@@{\phi})w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(1-k^{2}\cos^{2}@@{\phi})\deriv[2]{w}{\phi}+k^{2}\cos@@{\phi}\sin@@{\phi}\deriv{w}{\phi}+(h-\nu(\nu+1)k^{2}\cos^{2}@@{\phi})w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)* (cos((1)/(2)*Pi - JacobiAM(z, k)))^(2))*subs( temp=((1)/(2)*Pi - JacobiAM(z, k)), diff( w, temp$(2) ) )+ (k)^(2)* cos((1)/(2)*Pi - JacobiAM(z, k))*sin((1)/(2)*Pi - JacobiAM(z, k))*subs( temp=((1)/(2)*Pi - JacobiAM(z, k)), diff( w, temp$(1) ) )+(h - nu*(nu + 1)*(k)^(2)* (cos((1)/(2)*Pi - JacobiAM(z, k)))^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)* (Cos[Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]])^(2))*(D[w, {temp, 2}]/.temp-> (Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]))+ (k)^(2)* Cos[Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]]*Sin[Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]]*(D[w, {temp, 1}]/.temp-> (Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]))+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (Cos[Divide[1,2]*Pi - JacobiAmplitude[z, Power[k, 2]]])^(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: .9359870183-.3879581426*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5826053060-2.538844794*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.09035331946182407, -0.66279682113597]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[z, Rational[3, 2]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4348106213983929, 0.6227353307293972]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[z, Rational[3, 2]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.2#Ex1 29.2#Ex1] || [[Item:Q8579|<math>e_{1}+e_{2}+e_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{1}+e_{2}+e_{3} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">e[1]+ e[2]+ e[3] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[e, 1]+ Subscript[e, 2]+ Subscript[e, 3] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.2#Ex2 29.2#Ex2] || [[Item:Q8580|<math>\ifrac{(e_{2}-e_{3})}{(e_{1}-e_{3})} = k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ifrac{(e_{2}-e_{3})}{(e_{1}-e_{3})} = k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(e[2]- e[3])/(e[1]- e[3]) = (k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[Subscript[e, 2]- Subscript[e, 3],Subscript[e, 1]- Subscript[e, 3]] == (k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.2.E10 29.2.E10] || [[Item:Q8584|<math>{\deriv[2]{w}{\zeta}+\frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_{3}}\right)\deriv{w}{\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(\zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>{\deriv[2]{w}{\zeta}+\frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_{3}}\right)\deriv{w}{\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(\zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=(WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3])), diff( w, temp$(2) ) )+(1)/(2)*((1)/((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[1])+(1)/((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[2])+(1)/((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[3]))*subs( temp=(WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3])), diff( w, temp$(1) ) )+(((e[1]- e[3])*h + nu*(nu + 1)*e[3])- nu*(nu + 1)*(WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3])))/(4*((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[1])*((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[2])*((WeierstrassP((e[1]- e[3])^(- 1/2)*(z - I*EllipticCK(k)), g[2], 4*e[1]*e[2]*e[3]))- e[3]))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex3 29.3#Ex3] || [[Item:Q8602|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex4 29.3#Ex4] || [[Item:Q8603|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex5 29.3#Ex5] || [[Item:Q8605|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex6 29.3#Ex6] || [[Item:Q8606|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex7 29.3#Ex7] || [[Item:Q8607|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-3)(\nu+2p+4)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-3)(\nu+2p+4)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 3)*(nu + 2*p + 4)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 3)*(\[Nu]+ 2*p + 4)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex8 29.3#Ex8] || [[Item:Q8608|<math>\beta_{p} = (2p+2)^{2}(2-k^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = (2p+2)^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.3#Ex9 29.3#Ex9] || [[Item:Q8609|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E5 29.6.E5] || [[Item:Q8631|<math>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E6 29.6.E6] || [[Item:Q8632|<math>\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*A[0]+ sum(A[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E7 29.6.E7] || [[Item:Q8633|<math>\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n, \nu = 2n, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 2])/(A[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 2],Subscript[A, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex2 29.6#Ex2] || [[Item:Q8638|<math>\beta_{p} = 4p^{2}(2-k^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = 4p^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = 4*(p)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == 4*(p)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex3 29.6#Ex3] || [[Item:Q8639|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E12 29.6.E12] || [[Item:Q8640|<math>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*((1)/(2)*(C[0])^(2)+ sum((C[2*p])^(2), p = 1..infinity))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E13 29.6.E13] || [[Item:Q8641|<math>\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*C[0]+ sum(C[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E14 29.6.E14] || [[Item:Q8642|<math>\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 2])/(C[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 2],Subscript[C, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E20 29.6.E20] || [[Item:Q8648|<math>\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((A[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E21 29.6.E21] || [[Item:Q8649|<math>\sum_{p=0}^{\infty}A_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(A[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E22 29.6.E22] || [[Item:Q8650|<math>\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 1])/(A[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 1],Subscript[A, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex4 29.6#Ex4] || [[Item:Q8654|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex6 29.6#Ex6] || [[Item:Q8656|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E28 29.6.E28] || [[Item:Q8658|<math>\sum_{p=0}^{\infty}C_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}C_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(C[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E29 29.6.E29] || [[Item:Q8659|<math>\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 1])/(C[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 1],Subscript[C, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E35 29.6.E35] || [[Item:Q8665|<math>\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E36 29.6.E36] || [[Item:Q8666|<math>\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*B[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E37 29.6.E37] || [[Item:Q8667|<math>\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 1])/(B[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 1],Subscript[B, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex7 29.6#Ex7] || [[Item:Q8671|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex9 29.6#Ex9] || [[Item:Q8673|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E43 29.6.E43] || [[Item:Q8675|<math>\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*D[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E44 29.6.E44] || [[Item:Q8676|<math>\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 1])/(D[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 1],Subscript[D, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E50 29.6.E50] || [[Item:Q8682|<math>\sum_{p=1}^{\infty}B_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=1}^{\infty}B_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E51 29.6.E51] || [[Item:Q8683|<math>\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*B[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E52 29.6.E52] || [[Item:Q8684|<math>\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 2])/(B[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 2],Subscript[B, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex10 29.6#Ex10] || [[Item:Q8688|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex11 29.6#Ex11] || [[Item:Q8689|<math>\beta_{p} = (2p+2)^{2}(2-k^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = (2p+2)^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex12 29.6#Ex12] || [[Item:Q8690|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E57 29.6.E57] || [[Item:Q8691|<math>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*sum((D[2*p])^(2), p = 1..infinity)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E58 29.6.E58] || [[Item:Q8692|<math>\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*D[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E59 29.6.E59] || [[Item:Q8693|<math>\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+3, \nu = 2n+3, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 2])/(D[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 2],Subscript[D, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.7.E3 29.7.E3] || [[Item:Q8698|<math>\tau_{0} = \frac{1}{2^{3}}(1+k^{2})(1+p^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tau_{0} = \frac{1}{2^{3}}(1+k^{2})(1+p^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">tau[0] = (1)/((2)^(3))*(1 + (k)^(2))*(1 + (p)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Tau], 0] == Divide[1,(2)^(3)]*(1 + (k)^(2))*(1 + (p)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.7.E4 29.7.E4] || [[Item:Q8699|<math>\tau_{1} = \frac{p}{2^{6}}((1+k^{2})^{2}(p^{2}+3)-4k^{2}(p^{2}+5))</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tau_{1} = \frac{p}{2^{6}}((1+k^{2})^{2}(p^{2}+3)-4k^{2}(p^{2}+5))</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">tau[1] = (p)/((2)^(6))*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Tau], 1] == Divide[p,(2)^(6)]*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.7.E6 29.7.E6] || [[Item:Q8701|<math>\tau_{2} = \frac{1}{2^{10}}(1+k^{2})(1-k^{2})^{2}(5p^{4}+34p^{2}+9)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tau_{2} = \frac{1}{2^{10}}(1+k^{2})(1-k^{2})^{2}(5p^{4}+34p^{2}+9)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">tau[2] = (1)/((2)^(10))*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Tau], 2] == Divide[1,(2)^(10)]*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.7.E7 29.7.E7] || [[Item:Q8702|<math>\tau_{3} = \frac{p}{2^{14}}((1+k^{2})^{4}(33p^{4}+410p^{2}+405)-24k^{2}(1+k^{2})^{2}(7p^{4}+90p^{2}+95)+16k^{4}(9p^{4}+130p^{2}+173))</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tau_{3} = \frac{p}{2^{14}}((1+k^{2})^{4}(33p^{4}+410p^{2}+405)-24k^{2}(1+k^{2})^{2}(7p^{4}+90p^{2}+95)+16k^{4}(9p^{4}+130p^{2}+173))</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">tau[3] = (p)/((2)^(14))*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Tau], 3] == Divide[p,(2)^(14)]*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.7.E8 29.7.E8] || [[Item:Q8703|<math>\tau_{4} = \frac{1}{2^{16}}((1+k^{2})^{5}(63p^{6}+1260p^{4}+2943p^{2}+486)-8k^{2}(1+k^{2})^{3}(49p^{6}+1010p^{4}+2493p^{2}+432)+16k^{4}(1+k^{2})(35p^{6}+760p^{4}+2043p^{2}+378))</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tau_{4} = \frac{1}{2^{16}}((1+k^{2})^{5}(63p^{6}+1260p^{4}+2943p^{2}+486)-8k^{2}(1+k^{2})^{3}(49p^{6}+1010p^{4}+2493p^{2}+432)+16k^{4}(1+k^{2})(35p^{6}+760p^{4}+2043p^{2}+378))</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">tau[4] = (1)/((2)^(16))*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Tau], 4] == Divide[1,(2)^(16)]*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.8.E1 29.8.E1] || [[Item:Q8704|<math>x = k^{2}\Jacobiellsnk@{z}{k}\Jacobiellsnk@{z_{1}}{k}\Jacobiellsnk@{z_{2}}{k}\Jacobiellsnk@{z_{3}}{k}-\frac{k^{2}}{{k^{\prime}}^{2}}\Jacobiellcnk@{z}{k}\Jacobiellcnk@{z_{1}}{k}\Jacobiellcnk@{z_{2}}{k}\Jacobiellcnk@{z_{3}}{k}+\frac{1}{{k^{\prime}}^{2}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}\Jacobielldnk@{z_{2}}{k}\Jacobielldnk@{z_{3}}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = k^{2}\Jacobiellsnk@{z}{k}\Jacobiellsnk@{z_{1}}{k}\Jacobiellsnk@{z_{2}}{k}\Jacobiellsnk@{z_{3}}{k}-\frac{k^{2}}{{k^{\prime}}^{2}}\Jacobiellcnk@{z}{k}\Jacobiellcnk@{z_{1}}{k}\Jacobiellcnk@{z_{2}}{k}\Jacobiellcnk@{z_{3}}{k}+\frac{1}{{k^{\prime}}^{2}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}\Jacobielldnk@{z_{2}}{k}\Jacobielldnk@{z_{3}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = (k)^(2)* JacobiSN(x + y*I, k)*JacobiSN(x + y*I[1], k)*JacobiSN(x + y*I[2], k)*JacobiSN(x + y*I[3], k)-((k)^(2))/(1 - (k)^(2))*JacobiCN(x + y*I, k)*JacobiCN(x + y*I[1], k)*JacobiCN(x + y*I[2], k)*JacobiCN(x + y*I[3], k)+(1)/(1 - (k)^(2))*JacobiDN(x + y*I, k)*JacobiDN(x + y*I[1], k)*JacobiDN(x + y*I[2], k)*JacobiDN(x + y*I[3], k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == (k)^(2)* JacobiSN[x + y*I, (k)^2]*JacobiSN[Subscript[x + y*I, 1], (k)^2]*JacobiSN[Subscript[x + y*I, 2], (k)^2]*JacobiSN[Subscript[x + y*I, 3], (k)^2]-Divide[(k)^(2),1 - (k)^(2)]*JacobiCN[x + y*I, (k)^2]*JacobiCN[Subscript[x + y*I, 1], (k)^2]*JacobiCN[Subscript[x + y*I, 2], (k)^2]*JacobiCN[Subscript[x + y*I, 3], (k)^2]+Divide[1,1 - (k)^(2)]*JacobiDN[x + y*I, (k)^2]*JacobiDN[Subscript[x + y*I, 1], (k)^2]*JacobiDN[Subscript[x + y*I, 2], (k)^2]*JacobiDN[Subscript[x + y*I, 3], (k)^2]</syntaxhighlight> || Failure || Aborted || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [54 / 54]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[1.5, Times[Complex[1.6461554600232724, 0.45267954815584505], JacobiCN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiCN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiCN[Subscript[Complex[1.5, -1.5], 3], 4.0]], Times[Complex[0.619203045121549, 0.30086290583863873], JacobiDN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiDN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiDN[Subscript[Complex[1.5, -1.5], 3], 4.0]], Times[Complex[-2.0469921952210957, 3.2763330530501245], JacobiSN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiSN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiSN[Subscript[Complex[1.5, -1.5], 3], 4.0]]]
-Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.8.E2 29.8.E2] || [[Item:Q8705|<math>\mu w(z_{1})w(z_{2})w(z_{3}) = \int_{-2\compellintKk@@{k}}^{2\compellintKk@@{k}}\FerrersP[]{\nu}@{x}w(z)\diff{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu w(z_{1})w(z_{2})w(z_{3}) = \int_{-2\compellintKk@@{k}}^{2\compellintKk@@{k}}\FerrersP[]{\nu}@{x}w(z)\diff{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>mu*w*(x + y*I[1])*w*(x + y*I[2])*w*(x + y*I[3]) = int(LegendreP(nu, x)*w*((x + y*I)), (x + y*I) = - 2*EllipticK(k)..2*EllipticK(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu]*w*(Subscript[x + y*I, 1])*w*(Subscript[x + y*I, 2])*w*(Subscript[x + y*I, 3]) == Integrate[LegendreP[\[Nu], x]*w*((x + y*I)), {(x + y*I), - 2*EllipticK[(k)^2], 2*EllipticK[(k)^2]}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[-1.0, NIntegrate[Complex[2.8644916021274596, 0.010098545944192239]
-Test Values: {Complex[1.5, -1.5], DirectedInfinity[], DirectedInfinity[]}]], Times[Complex[-0.49999999999999994, 0.8660254037844387], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2], Subscript[Complex[1.5, -1.5], 3]]], {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Times[-1.0, NIntegrate[Complex[2.8644916021274596, 0.010098545944192239]
-Test Values: {Complex[1.5, -1.5], Times[-2, EllipticK[4]], Times[2, EllipticK[4]]}]], Times[Complex[-0.49999999999999994, 0.8660254037844387], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2], Subscript[Complex[1.5, -1.5], 3]]], {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.8.E3 29.8.E3] || [[Item:Q8706|<math>\mu = \frac{2\sigma\tau}{\Wronskian@{w,w_{2}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu = \frac{2\sigma\tau}{\Wronskian@{w,w_{2}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>mu = (2*sigma*tau)/((w)*diff(w[2], w)-diff(w, w)*(w[2]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu] == Divide[2*\[Sigma]*\[Tau],Wronskian[{w, Subscript[w, 2]}, w]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.598076212+1.500000000*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.866025404-1.232050808*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, w = 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: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-1.0000000000000002, -1.7320508075688772], Power[Plus[Complex[-0.8660254037844387, -0.49999999999999994], Times[Complex[0.8660254037844387, 0.49999999999999994], Derivative[1, 0][Subscript][Complex[0.8660254037844387, 0.49999999999999994], 2.0]]], -1]]]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, 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: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-1.0000000000000002, -1.7320508075688772], Power[Plus[Complex[0.4999999999999998, -0.8660254037844387], Times[Complex[0.8660254037844387, 0.49999999999999994], Derivative[1, 0][Subscript][Complex[0.8660254037844387, 0.49999999999999994], 2.0]]], -1]]]
-Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, 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/29.8#Ex1 29.8#Ex1] || [[Item:Q8707|<math>w(z+2\compellintKk@@{k}) = \sigma w(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(z+2\compellintKk@@{k}) = \sigma w(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(z + 2*EllipticK(k)) = sigma*w(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[z + 2*EllipticK[(k)^2]] == \[Sigma]*w[z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.038160455456161, -1.1586967532026022]
-Test Values: {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.8#Ex2 29.8#Ex2] || [[Item:Q8708|<math>w_{2}(z+2\compellintKk@@{k}) = \tau w(z)+\sigma w_{2}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w_{2}(z+2\compellintKk@@{k}) = \tau w(z)+\sigma w_{2}(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w[2](z + 2*EllipticK(k)) = tau*w(z)+ sigma*w[2](z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[w, 2][z + 2*EllipticK[(k)^2]] == \[Tau]*w[z]+ \[Sigma]*Subscript[w, 2][z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, 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[3.038160455456161, -2.1586967532026025]
-Test Values: {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.8.E6 29.8.E6] || [[Item:Q8710|<math>y = \frac{1}{k^{\prime}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = \frac{1}{k^{\prime}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = (1)/(sqrt(1 - (k)^(2)))*JacobiDN(x + y*I, k)*JacobiDN(x + y*I[1], k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == Divide[1,Sqrt[1 - (k)^(2)]]*JacobiDN[x + y*I, (k)^2]*JacobiDN[Subscript[x + y*I, 1], (k)^2]</syntaxhighlight> || Failure || Aborted || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [54 / 54]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-1.5, Times[Complex[-0.5211098390253335, 1.072491134351887], JacobiDN[Subscript[Complex[1.5, -1.5], 1], 4.0]]]
-Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.11.E1 29.11.E1] || [[Item:Q8721|<math>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2)+ (k)^(2)* (omega)^(2)* (JacobiSN(z, k))^(4))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (k)^(2)* \[Omega]^(2)* (JacobiSN[z, (k)^2])^(4))*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4970479804-.2136667430*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5039614158-1.687364305*I
-Test Values: {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4970479802306743, -0.21366674241821534]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.5039614145885605, -1.6873643054323533]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.12.E10 29.12.E10] || [[Item:Q8731|<math>0 < \xi_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < \xi_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < xi[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < Subscript[\[Xi], 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.12.E12 29.12.E12] || [[Item:Q8733|<math>0 \leq t_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 \leq t_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= t[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 <= Subscript[t, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.14.E3 29.14.E3] || [[Item:Q8737|<math>w(s,t) = \Jacobiellsnk^{2}@{\compellintKk@@{k}+\iunit t}{k}-\Jacobiellsnk^{2}@{s}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>w(s,t) = \Jacobiellsnk^{2}@{\compellintKk@@{k}+\iunit t}{k}-\Jacobiellsnk^{2}@{s}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>w(s , t) = (JacobiSN(EllipticK(k)+ I*t, k))^(2)- (JacobiSN(s, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>w[s , t] == (JacobiSN[EllipticK[(k)^2]+ I*t, (k)^2])^(2)- (JacobiSN[s, (k)^2])^(2)</syntaxhighlight> || Failure || Failure || Error || Error
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E5 29.15.E5] || [[Item:Q8750|<math>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}A_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}A_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E6 29.15.E6] || [[Item:Q8751|<math>\tfrac{1}{2}A_{0}+\sum_{p=1}^{n}A_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}+\sum_{p=1}^{n}A_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*A[0]+ sum(A[2*p], p = 1..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E10 29.15.E10] || [[Item:Q8755|<math>\sum_{p=0}^{n}A_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}A_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((A[2*p + 1])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E11 29.15.E11] || [[Item:Q8756|<math>\sum_{p=0}^{n}A_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}A_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(A[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[A, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E15 29.15.E15] || [[Item:Q8760|<math>\sum_{p=0}^{n}B_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}B_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 1])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E16 29.15.E16] || [[Item:Q8761|<math>\sum_{p=0}^{n}(2p+1)B_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+1)B_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*B[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E20 29.15.E20] || [[Item:Q8765|<math>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{n}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{n-1}C_{2p}C_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{n}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{n-1}C_{2p}C_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*((1)/(2)*(C[0])^(2)+ sum((C[2*p])^(2), p = 1..n))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..n - 1) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, n}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, n - 1}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E21 29.15.E21] || [[Item:Q8766|<math>\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*C[0]+ sum(C[2*p], p = 1..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E25 29.15.E25] || [[Item:Q8770|<math>\sum_{p=0}^{n}B_{2p+2}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}B_{2p+2}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 2])^(2), p = 0..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E26 29.15.E26] || [[Item:Q8771|<math>\sum_{p=0}^{n}(2p+2)B_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+2)B_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*B[2*p + 2], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E31 29.15.E31] || [[Item:Q8776|<math>\sum_{p=0}^{n}C_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}C_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(C[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[C, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E36 29.15.E36] || [[Item:Q8781|<math>\sum_{p=0}^{n}(2p+1)D_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+1)D_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*D[2*p + 1], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E40 29.15.E40] || [[Item:Q8785|<math>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=0}^{n}D_{2p+2}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{n}D_{2p}D_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=0}^{n}D_{2p+2}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{n}D_{2p}D_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*sum((D[2*p + 2])^(2), p = 0..n)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..n) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, n}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.15.E41 29.15.E41] || [[Item:Q8786|<math>\sum_{p=0}^{n}(2p+2)D_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{n}(2p+2)D_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*D[2*p + 2], p = 0..n) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.18#Ex1 29.18#Ex1] || [[Item:Q8798|<math>x = kr\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = kr\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = k*r*JacobiSN(beta, k)*JacobiSN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == k*r*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.206882914
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.742014676
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, x = 3/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.5758629567327462, 0.3306870492079255]
-Test Values: {Rule[k, 1], Rule[r, -1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.8681877710203056, -0.008479026933090933]
-Test Values: {Rule[k, 2], Rule[r, -1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex2 29.18#Ex2] || [[Item:Q8799|<math>y = \iunit\frac{k}{k^{\prime}}r\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = \iunit\frac{k}{k^{\prime}}r\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = I*(k)/(sqrt(1 - (k)^(2)))*r*JacobiCN(beta, k)*JacobiCN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == I*Divide[k,Sqrt[1 - (k)^(2)]]*r*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.500000000+Float(infinity)*I
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, y = -3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .24058897e-1
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, y = -3/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[r, -1.5], Rule[y, -1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.25004703976217724, 0.0247093927223503]
-Test Values: {Rule[k, 2], Rule[r, -1.5], Rule[y, -1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex3 29.18#Ex3] || [[Item:Q8800|<math>z = \frac{1}{k^{\prime}}r\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \frac{1}{k^{\prime}}r\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = (1)/(sqrt(1 - (k)^(2)))*r*JacobiDN(beta, k)*JacobiDN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Divide[1,Sqrt[1 - (k)^(2)]]*r*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+.5000000000*I
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8660254040+.8623901524*I
-Test Values: {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.6104237277084903, 0.46270316084846885]
-Test Values: {Rule[k, 2], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.18#Ex4 29.18#Ex4] || [[Item:Q8801|<math>r \geq 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>r \geq 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r >= 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r >= 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.18#Ex7 29.18#Ex7] || [[Item:Q8804|<math>0 \leq \gamma</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>0 \leq \gamma</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>0 <= gamma</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 <= \[Gamma]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. <= -1.500000000
-Test Values: {gamma = -3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. <= -.5000000000
-Test Values: {gamma = -1/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[0.8660254037844387, 0.49999999999999994]]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[-0.4999999999999998, 0.8660254037844387]]
-Test Values: {Rule[γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex7 29.18#Ex7] || [[Item:Q8804|<math>\gamma \leq 4\compellintKk@@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\gamma \leq 4\compellintKk@@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>gamma <= 4*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Gamma] <= 4*EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[]]
-Test Values: {Rule[k, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.8660254037844387, 0.49999999999999994], Complex[3.3715007096251925, -4.313031294999287]]
-Test Values: {Rule[k, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.18.E4 29.18.E4] || [[Item:Q8805|<math>u(r,\beta,\gamma) = u_{1}(r)u_{2}(\beta)u_{3}(\gamma)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u(r,\beta,\gamma) = u_{1}(r)u_{2}(\beta)u_{3}(\gamma)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u(r , beta , gamma) = u[1](r)* u[2](beta)* u[3](gamma)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[r , \[Beta], \[Gamma]] == Subscript[u, 1][r]* Subscript[u, 2][\[Beta]]* Subscript[u, 3][\[Gamma]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/29.18.E5 29.18.E5] || [[Item:Q8806|<math>\deriv{}{r}\left(r^{2}\deriv{u_{1}}{r}\right)+(\omega^{2}r^{2}-\nu(\nu+1))u_{1} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{r}\left(r^{2}\deriv{u_{1}}{r}\right)+(\omega^{2}r^{2}-\nu(\nu+1))u_{1} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(((r)^(2)* diff(u[1], r))+((omega)^(2)* (r)^(2)- nu*(nu + 1))*u[1], r) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[((r)^(2)* D[Subscript[u, 1], r])+(\[Omega]^(2)* (r)^(2)- \[Nu]*(\[Nu]+ 1))*Subscript[u, 1], r] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9701216577e-9-3.000000003*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, r = -3/2, u[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.000000003-.1039230485e-8*I
-Test Values: {nu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, r = -3/2, u[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[-4.440892098500626*^-16, -3.0]
-Test Values: {Rule[r, -1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.0, -1.1102230246251565*^-15]
-Test Values: {Rule[r, -1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18.E6 29.18.E6] || [[Item:Q8807|<math>\deriv[2]{u_{2}}{\beta}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\beta}{k})u_{2} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u_{2}}{\beta}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\beta}{k})u_{2} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u[2], [beta$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(beta, k))^(2))*u[2] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[u, 2], {\[Beta], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Beta], (k)^2])^(2))*Subscript[u, 2] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9035331887e-1-.6627968211*I
-Test Values: {beta = 3/2, h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, u[2] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4348106217+.6227353309*I
-Test Values: {beta = 3/2, h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, u[2] = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.09035331946182387, -0.6627968211359702]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[β, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4348106213983929, 0.6227353307293972]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[β, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18.E7 29.18.E7] || [[Item:Q8808|<math>\deriv[2]{u_{3}}{\gamma}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\gamma}{k})u_{3} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{u_{3}}{\gamma}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\gamma}{k})u_{3} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(u[3], [gamma$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(gamma, k))^(2))*u[3] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Subscript[u, 3], {\[Gamma], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Gamma], (k)^2])^(2))*Subscript[u, 3] == 0</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9359870178672973, -0.3879581414973573]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.5826053037338313, -2.538844793552361]
-Test Values: {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex8 29.18#Ex8] || [[Item:Q8809|<math>x = k\Jacobiellsnk@{\alpha}{k}\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x = k\Jacobiellsnk@{\alpha}{k}\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>x = k*JacobiSN(alpha, k)*JacobiSN(beta, k)*JacobiSN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == k*JacobiSN[\[Alpha], (k)^2]*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.073444110
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.470871115
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8507896823681017, -0.1995472033956852]
-Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.4556849214429664, 0.0010205356456730495]
-Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex9 29.18#Ex9] || [[Item:Q8810|<math>y = -\frac{k}{k^{\prime}}\Jacobiellcnk@{\alpha}{k}\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>y = -\frac{k}{k^{\prime}}\Jacobiellcnk@{\alpha}{k}\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>y = -(k)/(sqrt(1 - (k)^(2)))*JacobiCN(alpha, k)*JacobiCN(beta, k)*JacobiCN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == -Divide[k,Sqrt[1 - (k)^(2)]]*JacobiCN[\[Alpha], (k)^2]*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.500000000-.9993433457*I
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.4837977605404604, -0.8196088589670207]
-Test Values: {Rule[k, 2], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/29.18#Ex10 29.18#Ex10] || [[Item:Q8811|<math>z = \frac{\iunit}{kk^{\prime}}\Jacobielldnk@{\alpha}{k}\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = \frac{\iunit}{kk^{\prime}}\Jacobielldnk@{\alpha}{k}\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = (I)/(k*sqrt(1 - (k)^(2)))*JacobiDN(alpha, k)*JacobiDN(beta, k)*JacobiDN(gamma, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == Divide[I,k*Sqrt[1 - (k)^(2)]]*JacobiDN[\[Alpha], (k)^2]*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040-Float(infinity)*I
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7533782555+.5000000000*I
-Test Values: {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[k, 1], 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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8776189378612058, 0.7313924592922922]
-Test Values: {Rule[k, 2], 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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.18.E10 29.18.E10] || [[Item:Q8814|<math>u(\alpha,\beta,\gamma) = u_{1}(\alpha)u_{2}(\beta)u_{3}(\gamma)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u(\alpha,\beta,\gamma) = u_{1}(\alpha)u_{2}(\beta)u_{3}(\gamma)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u(alpha , beta , gamma) = u[1](alpha)* u[2](beta)* u[3](gamma)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[\[Alpha], \[Beta], \[Gamma]] == Subscript[u, 1][\[Alpha]]* Subscript[u, 2][\[Beta]]* Subscript[u, 3][\[Gamma]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|}
 </div>

Results of Lamé Functions: Difference between revisions

Latest revision as of 17:52, 25 May 2021

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