Results of Jacobian Elliptic Functions: Difference between revisions

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; Notation : [[22.1|22.1 Special Notation]]<br>
! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
; Properties : [[22.2|22.2 Definitions]]<br>[[22.3|22.3 Graphics]]<br>[[22.4|22.4 Periods, Poles, and Zeros]]<br>[[22.5|22.5 Special Values]]<br>[[22.6|22.6 Elementary Identities]]<br>[[22.7|22.7 Landen Transformations]]<br>[[22.8|22.8 Addition Theorems]]<br>[[22.9|22.9 Cyclic Identities]]<br>[[22.10|22.10 Maclaurin Series]]<br>[[22.11|22.11 Fourier and Hyperbolic Series]]<br>[[22.12|22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial
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Fractions: Eisenstein Series]]<br>[[22.13|22.13 Derivatives and Differential Equations]]<br>[[22.14|22.14 Integrals]]<br>[[22.15|22.15 Inverse Functions]]<br>[[22.16|22.16 Related Functions]]<br>[[22.17|22.17 Moduli Outside the Interval [0,1]]]<br>
| [https://dlmf.nist.gov/22.2#Ex1 22.2#Ex1] || [[Item:Q6922|<math>k = \frac{\Jacobithetaq{2}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>k = ((JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))/((JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>k == Divide[(EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2),(EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2)]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 3]
; Applications : [[22.18|22.18 Mathematical Applications]]<br>[[22.19|22.19 Physical Applications]]<br>
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; Computation : [[22.20|22.20 Methods of Computation]]<br>[[22.21|22.21 Tables]]<br>[[22.22|22.22 Software]]<br>
| [https://dlmf.nist.gov/22.2#Ex2 22.2#Ex2] || [[Item:Q6923|<math>k^{\prime} = \frac{\Jacobithetaq{4}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sqrt(1 - (k)^(2)) = ((JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))/((JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sqrt[1 - (k)^(2)] == Divide[(EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2),(EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2)]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 3]
</div>
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| [https://dlmf.nist.gov/22.2#Ex3 22.2#Ex3] || [[Item:Q6924|<math>\compellintKk@{k} = \frac{\pi}{2}\Jacobithetaq{3}^{2}@{0}{q}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(k) = (Pi)/(2)*(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(k)^2] == Divide[Pi,2]*(EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
Test Values: {Rule[k, 1]}</syntaxhighlight><br></div></div>
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| [https://dlmf.nist.gov/22.2.E3 22.2.E3] || [[Item:Q6925|<math>\zeta = \frac{\pi z}{2\compellintKk@{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>zeta = (Pi*z)/(2*EllipticK(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Zeta] == Divide[Pi*z,2*EllipticK[(k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.7059984047169785, -0.6365247818792681]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E4 22.2.E4] || [[Item:Q6926|<math>\Jacobiellsnk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = (JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1017958925630662, 9.78035129055685*^-4]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.08293092681074243, -0.5359189266558633]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E4 22.2.E4] || [[Item:Q6926|<math>\frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.1017958925630662, -9.780351290556814*^-4]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.08293092681074243, 0.5359189266558634]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E5 22.2.E5] || [[Item:Q6927|<math>\Jacobiellcnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = (JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.08257811120249814, 0.0027270134984790223]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.13231049687767538, 0.2777560839806882]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E5 22.2.E5] || [[Item:Q6927|<math>\frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnck@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiNC(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiNC[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.08257811120249814, -0.002727013498479031]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.13231049687767538, -0.2777560839806882]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E6 22.2.E6] || [[Item:Q6928|<math>\Jacobielldnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = (JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.11217526698173597, -1.5044574583405517]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.6119897435833945, -2.3508894631681736]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E6 22.2.E6] || [[Item:Q6928|<math>\frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellndk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiND(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiND[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.112175266981736, 1.5044574583405517]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.6119897435833943, 2.350889463168173]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/22.2.E7 22.2.E7] || [[Item:Q6929|<math>\Jacobiellsdk@{z}{k} = \frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(z, k) = ((JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k)))*JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[z, (k)^2] == Divide[(EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2),EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]*EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [138 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.10264566281694597, 1.7190366283522571]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.005017214212665183, 0.8218706074973681]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E7 22.2.E7] || [[Item:Q6929|<math>\frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))^(2))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k)))*JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiDS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]])^(2),EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]*EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiDS[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [138 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.1026456628169461, -1.7190366283522573]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.005017214212665148, -0.8218706074973681]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E8 22.2.E8] || [[Item:Q6930|<math>\Jacobiellcdk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(z, k) = (JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[z, (k)^2] == Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.23207264303523145, 2.174081147069575]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3131092646447684, 1.178043032175558]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E8 22.2.E8] || [[Item:Q6930|<math>\frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldck@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta3(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiDC(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[3, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiDC[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.23207264303523142, -2.174081147069575]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.3131092646447683, -1.178043032175558]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E9 22.2.E9] || [[Item:Q6931|<math>\Jacobiellsck@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(z, k) = (JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[z, (k)^2] == Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.2180891710993932, -0.009050644683206828]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.13880139985550538, -0.6261898650931494]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E9 22.2.E9] || [[Item:Q6931|<math>\frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}} = \frac{1}{\Jacobiellcsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiTheta3(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta4(0, exp(- Pi*EllipticCK(k)/EllipticK(k))))*(JacobiTheta1(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k))))/(JacobiTheta2(zeta, exp(- Pi*EllipticCK(k)/EllipticK(k)))) = (1)/(JacobiCS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[EllipticTheta[3, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[4, 0, Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]]*Divide[EllipticTheta[1, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]],EllipticTheta[2, \[Zeta], Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]]]] == Divide[1,JacobiCS[z, (k)^2]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [140 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.2180891710993933, 0.009050644683206842]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.13880139985550533, 0.6261898650931494]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.2.E11 22.2.E11] || [[Item:Q6933|<math>\genJacobiellk{p}{q}@{z}{k} = \ifrac{\Jacobithetatau{p}@{z}{\tau}}{\Jacobithetatau{q}@{z}{\tau}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))* z*k = (JacobiThetap(z,exp(I*Pi*tau)))/(JacobiThetaexp(- Pi*EllipticCK(k)/EllipticK(k))(z,exp(I*Pi*tau)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])* z*k == Divide[EllipticTheta[p, z, Exp[I*Pi*(\[Tau])]],EllipticTheta[Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]], z, Exp[I*Pi*(\[Tau])]]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[Complex[0.5000000000000001, 0.8660254037844386], genJacobiellk], Times[Complex[-0.31964140165035193, 0.682988488811487], EllipticTheta[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.1897367196265697, 0.08493465422971205]]]]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Times[Complex[0.26976733074627424, -0.3419272748333145], genJacobiellk], Times[-1.0, EllipticTheta[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.1897367196265697, 0.08493465422971205]], Power[EllipticTheta[Power[E, Times[-1, Pi, EllipticK[-3], Power[EllipticK[4], -1]]], Complex[0.8660254037844387, 0.49999999999999994], Complex</div></div>
|-
| [https://dlmf.nist.gov/22.2.E12 22.2.E12] || [[Item:Q6934|<math>\tau = \ifrac{\iunit\ccompellintKk@{k}}{\compellintKk@{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>tau = (I*EllipticCK(k))/(EllipticK(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Tau] == Divide[I*EllipticK[1-(k)^2],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: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.4867361401447923, 0.0147898206680519]
Test Values: {Rule[k, 2], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || [[Item:Q6935|<math>\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2) = (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2) == (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || [[Item:Q6935|<math>k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || [[Item:Q6936|<math>1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>1 + (JacobiCS(z, k))^(2) = (k)^(2)+ (JacobiDS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 + (JacobiCS[z, (k)^2])^(2) == (k)^(2)+ (JacobiDS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || [[Item:Q6936|<math>k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS(z, k))^(2) = (JacobiNS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS[z, (k)^2])^(2) == (JacobiNS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || [[Item:Q6937|<math>{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)+ 1 == (JacobiDC[z, (k)^2])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7126235439-1.151829144*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .144618294+.733840068e-1*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7126235442208428, -1.1518291435850532]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.14461829395996295, 0.07338400615035004]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || [[Item:Q6937|<math>\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDC(z, k))^(2) = 1 - (k)^(2)*(JacobiNC(z, k))^(2)+ (k)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDC[z, (k)^2])^(2) == 1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2)+ (k)^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .287376456+1.151829144*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .855381706-.733840068e-1*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.4338548818798933, 0.22015201845104385]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || [[Item:Q6938|<math>-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(2) = (k)^(2)*((JacobiCD(z, k))^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2) == (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.672736560+.4694177821*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2873764557791572, -1.1518291435850532]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[4.672736560761239, 0.46941777772332965]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || [[Item:Q6938|<math>k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD(z, k))^(2)- 1) = 1 - (k)^(2)*(1 - (JacobiND(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) == 1 - (k)^(2)*(1 - (JacobiND[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.168184140+.1173544454*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2873764557791576, -1.1518291435850534]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1681841401903128, 0.11735444443083248]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E5 22.6.E5] || [[Item:Q6939|<math>\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(2*z, k) = (2*JacobiSN(z, k)*JacobiCN(z, k)*JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[2*z, (k)^2] == Divide[2*JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]*JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || [[Item:Q6940|<math>\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(2*z, k) = ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[2*z, (k)^2] == Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || [[Item:Q6940|<math>\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiCN(z, k))^(4)-1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiCN[z, (k)^2])^(4)-1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8884947272+1.003906290*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 12.71128264-7.657522619*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.88849472735544, 1.0039062900432163]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[12.711282681655987, -7.657522555241993]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || [[Item:Q6941|<math>\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(2*z, k) = ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[2*z, (k)^2] == Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || [[Item:Q6941|<math>\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiDN(z, k))^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.000000000+0.*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -29.55188938+16.70732208*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0000000000000002, -1.1102230246251565*^-16]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-29.55188948724943, 16.70732193870979]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E8 22.6.E8] || [[Item:Q6942|<math>\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(2*z, k) = ((JacobiCD(z, k))^(2)-1 - (k)^(2)*(JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[2*z, (k)^2] == Divide[(JacobiCD[z, (k)^2])^(2)-1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6073373021+.4789879505*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5744703200+.1556450229*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6073373022896961, 0.47898795042922426]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5744703197186243, 0.15564502146829437]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E9 22.6.E9] || [[Item:Q6943|<math>\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(2*z, k) = (2*JacobiSD(z, k)*JacobiCD(z, k)*JacobiND(z, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[2*z, (k)^2] == Divide[2*JacobiSD[z, (k)^2]*JacobiCD[z, (k)^2]*JacobiND[z, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.189544202+1.637439170*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5756484648e-1+.8251147581*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.189544200468709, 1.6374391687321102]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.05756484595277844, 0.825114758131751]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E10 22.6.E10] || [[Item:Q6944|<math>\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(2*z, k) = ((JacobiND(z, k))^(2)+ (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[2*z, (k)^2] == Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.247856974+1.526848242*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1237018962-.8644962079e-1*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2478569728519586, 1.5268482411210251]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.1237018961558749, -0.0864496199922923]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E11 22.6.E11] || [[Item:Q6945|<math>\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(2*z, k) = ((JacobiDC(z, k))^(2)+1 - (k)^(2)*(JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[2*z, (k)^2] == Divide[(JacobiDC[z, (k)^2])^(2)+1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.456738398+.1506627644*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4.350355103-.3722352376e-1*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.456738400104645, 0.15066276425673586]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-4.350355102633989, -0.03722352327899177]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E12 22.6.E12] || [[Item:Q6946|<math>\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(2*z, k) = ((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2)* (JacobiDC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[2*z, (k)^2] == Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2)* (JacobiDC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.356171111+.335718656*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3210452605+.1984107752*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.356171110076661, 0.3357186535359711]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.3210452604978905, 0.19841077324251138]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E13 22.6.E13] || [[Item:Q6947|<math>\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(2*z, k) = (2*JacobiSC(z, k)*JacobiDC(z, k)*JacobiNC(z, k))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[2*z, (k)^2] == Divide[2*JacobiSC[z, (k)^2]*JacobiDC[z, (k)^2]*JacobiNC[z, (k)^2],1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.370082581+.423198902*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2742031773e-1-2.068263955*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3700825790735573, 0.42319889849983916]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.027420317388659004, -2.068263954207401]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E14 22.6.E14] || [[Item:Q6948|<math>\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(2*z, k) = ((JacobiNS(z, k))^(4)- (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[2*z, (k)^2] == Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E15 22.6.E15] || [[Item:Q6949|<math>\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(2*z, k) = ((k)^(2)*1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[2*z, (k)^2] == Divide[(k)^(2)*1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1079800431-2.783083843*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.118875072+.736498896*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.10798004208618706, -2.7830838428160787]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-6.118875073385709, 0.7364988890066191]
Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E16 22.6.E16] || [[Item:Q6950|<math>\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(2*z, k) = ((JacobiCS(z, k))^(4)-1 - (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[2*z, (k)^2] == Divide[(JacobiCS[z, (k)^2])^(4)-1 - (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.528217681e-1+.9827060369*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7198669539e-1+1.855389227*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.05282176850410922, 0.9827060372847245]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.07198669472412605, 1.8553892285440545]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E17 22.6.E17] || [[Item:Q6951|<math>\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(2*z, k))/(1 + JacobiCN(2*z, k)) = ((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[2*z, (k)^2],1 + JacobiCN[2*z, (k)^2]] == Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E18 22.6.E18] || [[Item:Q6952|<math>\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(2*z, k))/(1 + JacobiDN(2*z, k)) = ((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[2*z, (k)^2],1 + JacobiDN[2*z, (k)^2]] == Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN((1)/(2)*z, k))^(2) = (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[Divide[1,2]*z, (k)^2])^(2) == Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) = (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] == Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)-1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]-1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+.1810063706*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.050510101+1.261106800*I
Test Values: {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 [21 / 21]<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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.0505101013872702, 1.2611068009765694]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiCN((1)/(2)*z, k))^(2) = (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiCN[Divide[1,2]*z, (k)^2])^(2) == Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.140351911+.1810063706*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.153509822-.96502865e-2*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.140351911309134, 0.18100637055769858]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.1535098215093709, -0.009650286433913441]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.304876195-.1041070951*I
Test Values: {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 [21 / 21]<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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.304876194963382, -0.10410709518022829]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) = (1 - (k)^(2)*(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .315116621e-1+.1309658139*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.03151166205333389, 0.13096581390504758]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDN((1)/(2)*z, k))^(2) = ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDN[Divide[1,2]*z, (k)^2])^(2) == Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) = (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3945345066-.4550295262*I
Test Values: {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 [21 / 21]<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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.39453450618395575, -0.455029526456568]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) = (1 - (k)^(2)*(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3624296261+.6038808640*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3624296259668921, 0.6038808642712606]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*(q)^(2)* (1)/(2)*zk = (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*(q)^(2)* Divide[1,2]*zk == Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) = (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k] == Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[0.7500000000000001, 0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[1.5000000000000002, 0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[</div></div>
|-
| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) = (genJacobiellk(p)*r* z*k + 1)/(genJacobiellk(q)*r* z*k + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k] == Divide[genJacobiellk[p]*r* z*k + 1,genJacobiellk[q]*r* z*k + 1]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[Complex[-0.7500000000000001, -0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[Complex[-1.5000000000000002, -0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.7.E2 22.7.E2] || [[Item:Q6958|<math>\Jacobiellsnk@{z}{k} = \frac{(1+k_{1})\Jacobiellsnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = ((1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))*JacobiSN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))*(JacobiSN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]]))*JacobiSN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2],1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])*(JacobiSN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.7.E3 22.7.E3] || [[Item:Q6959|<math>\Jacobiellcnk@{z}{k} = \frac{\Jacobiellcnk@{z/(1+k_{1})}{k_{1}}\Jacobielldnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = (JacobiCN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))*JacobiDN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))*(JacobiSN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[JacobiCN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2]*JacobiDN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2],1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])*(JacobiSN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.7.E4 22.7.E4] || [[Item:Q6960|<math>\Jacobielldnk@{z}{k} = \frac{\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}-(1-k_{1})}{1+k_{1}-\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = ((JacobiDN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))^(2)-(1 -((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))))/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))- (JacobiDN(z/(1 +((1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2))))), (1 -sqrt(1 - (k)^(2)))/(1 +sqrt(1 - (k)^(2)))))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[(JacobiDN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2])^(2)-(1 -(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])),1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])- (JacobiDN[z/(1 +(Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])), (Divide[1 -Sqrt[1 - (k)^(2)],1 +Sqrt[1 - (k)^(2)]])^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.7.E6 22.7.E6] || [[Item:Q6963|<math>\Jacobiellsnk@{z}{k} = \frac{(1+k_{2}^{\prime})\Jacobiellsnk@{z/(1+k_{2}^{\prime})}{k_{2}}\Jacobiellcnk@{z/(1+k_{2}^{\prime})}{k_{2}}}{\Jacobielldnk@{z/(1+k_{2}^{\prime})}{k_{2}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = ((1 +((1 - k)/(1 + k)))*JacobiSN(z/(1 +((1 - k)/(1 + k))), k[2])*JacobiCN(z/(1 +((1 - k)/(1 + k))), k[2]))/(JacobiDN(z/(1 +((1 - k)/(1 + k))), k[2]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[(1 +(Divide[1 - k,1 + k]))*JacobiSN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2]*JacobiCN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2],JacobiDN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2320130981+.1889825613*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4896247760+.2144288908*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[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 [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.23201309774017753, 0.18898256119227738]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.4896247756050003, 0.2144288910337357]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.7.E7 22.7.E7] || [[Item:Q6964|<math>\Jacobiellcnk@{z}{k} = \frac{(1+k_{2}^{\prime})(\Jacobielldnk^{2}@{z/(1+k_{2}^{\prime})}{k_{2}}-k_{2}^{\prime})}{k_{2}^{2}\Jacobielldnk@{z/(1+k_{2}^{\prime})}{k_{2}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = ((1 +((1 - k)/(1 + k)))*((JacobiDN(z/(1 +((1 - k)/(1 + k))), k[2]))^(2)-((1 - k)/(1 + k))))/((k[2])^(2)*JacobiDN(z/(1 +((1 - k)/(1 + k))), k[2]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[(1 +(Divide[1 - k,1 + k]))*((JacobiDN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2])^(2)-(Divide[1 - k,1 + k])),(Subscript[k, 2])^(2)*JacobiDN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3582173507+.1286198012*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5427357897+.8396234046e-1*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[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 [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5228144818495482, 0.8542847397966109]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.6630406190754804, 0.41475216363716894]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.7.E8 22.7.E8] || [[Item:Q6965|<math>\Jacobielldnk@{z}{k} = \frac{(1-k_{2}^{\prime})(\Jacobielldnk^{2}@{z/(1+k_{2}^{\prime})}{k_{2}}+k_{2}^{\prime})}{k_{2}^{2}\Jacobielldnk@{z/(1+k_{2}^{\prime})}{k_{2}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = ((1 -((1 - k)/(1 + k)))*((JacobiDN(z/(1 +((1 - k)/(1 + k))), k[2]))^(2)+((1 - k)/(1 + k))))/((k[2])^(2)*JacobiDN(z/(1 +((1 - k)/(1 + k))), k[2]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[(1 -(Divide[1 - k,1 + k]))*((JacobiDN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2])^(2)+(Divide[1 - k,1 + k])),(Subscript[k, 2])^(2)*JacobiDN[z/(1 +(Divide[1 - k,1 + k])), (Subscript[k, 2])^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3582173507+.1286198012*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[2] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2544342076-.6669510446*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k[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 [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5228144818495482, 0.8542847397966109]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.18687780488878028, -0.30624830191491115]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[k, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E1 22.8.E1] || [[Item:Q6966|<math>\Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(u + v, k) = (JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/22.8.E2 22.8.E2] || [[Item:Q6967|<math>\Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}-\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(u + v, k) = (JacobiCN(u, k)*JacobiCN(v, k)- JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[u + v, (k)^2] == Divide[JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]- JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/22.8.E3 22.8.E3] || [[Item:Q6968|<math>\Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobielldnk@@{u}{k}\Jacobielldnk@@{v}{k}-k^{2}\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(u + v, k) = (JacobiDN(u, k)*JacobiDN(v, k)- (k)^(2)* JacobiSN(u, k)*JacobiCN(u, k)*JacobiSN(v, k)*JacobiCN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[u + v, (k)^2] == Divide[JacobiDN[u, (k)^2]*JacobiDN[v, (k)^2]- (k)^(2)* JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/22.8.E4 22.8.E4] || [[Item:Q6969|<math>\Jacobiellcdk@@{(u+v)}{k} = \frac{\Jacobiellcdk@@{u}{k}\Jacobiellcdk@@{v}{k}-{k^{\prime}}^{2}\Jacobiellsdk@@{u}{k}\Jacobiellndk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellndk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(u + v, k) = (JacobiCD(u, k)*JacobiCD(v, k)-1 - (k)^(2)*JacobiSD(u, k)*JacobiND(u, k)*JacobiSD(v, k)*JacobiND(v, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[u + v, (k)^2] == Divide[JacobiCD[u, (k)^2]*JacobiCD[v, (k)^2]-1 - (k)^(2)*JacobiSD[u, (k)^2]*JacobiND[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiND[v, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6073373021+.4789879505*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5744703200+.1556450229*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 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[0.6073373022896961, 0.47898795042922426]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.5744703197186243, 0.15564502146829437]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E5 22.8.E5] || [[Item:Q6970|<math>\Jacobiellsdk@@{(u+v)}{k} = \frac{\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{v}{k}\Jacobiellndk@@{v}{k}+\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{u}{k}\Jacobiellndk@@{u}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(u + v, k) = (JacobiSD(u, k)*JacobiCD(v, k)*JacobiND(v, k)+ JacobiSD(v, k)*JacobiCD(u, k)*JacobiND(u, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[u + v, (k)^2] == Divide[JacobiSD[u, (k)^2]*JacobiCD[v, (k)^2]*JacobiND[v, (k)^2]+ JacobiSD[v, (k)^2]*JacobiCD[u, (k)^2]*JacobiND[u, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.189544202+1.637439170*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5756484648e-1+.8251147581*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 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 [270 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.189544200468709, 1.6374391687321102]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.05756484595277844, 0.825114758131751]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E6 22.8.E6] || [[Item:Q6971|<math>\Jacobiellndk@@{(u+v)}{k} = \frac{\Jacobiellndk@@{u}{k}\Jacobiellndk@@{v}{k}+k^{2}\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(u + v, k) = (JacobiND(u, k)*JacobiND(v, k)+ (k)^(2)* JacobiSD(u, k)*JacobiCD(u, k)*JacobiSD(v, k)*JacobiCD(v, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[u + v, (k)^2] == Divide[JacobiND[u, (k)^2]*JacobiND[v, (k)^2]+ (k)^(2)* JacobiSD[u, (k)^2]*JacobiCD[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiCD[v, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.247856974+1.526848242*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1237018962-.8644962079e-1*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2478569728519586, 1.5268482411210251]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.1237018961558749, -0.0864496199922923]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E7 22.8.E7] || [[Item:Q6972|<math>\Jacobielldck@@{(u+v)}{k} = \frac{\Jacobielldck@@{u}{k}\Jacobielldck@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsck@@{u}{k}\Jacobiellnck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobiellnck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(u + v, k) = (JacobiDC(u, k)*JacobiDC(v, k)+1 - (k)^(2)*JacobiSC(u, k)*JacobiNC(u, k)*JacobiSC(v, k)*JacobiNC(v, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[u + v, (k)^2] == Divide[JacobiDC[u, (k)^2]*JacobiDC[v, (k)^2]+1 - (k)^(2)*JacobiSC[u, (k)^2]*JacobiNC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiNC[v, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.456738398+.1506627644*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4.350355103-.3722352376e-1*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.456738400104645, 0.15066276425673586]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-4.350355102633989, -0.03722352327899177]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E8 22.8.E8] || [[Item:Q6973|<math>\Jacobiellnck@@{(u+v)}{k} = \frac{\Jacobiellnck@@{u}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{u}{k}\Jacobielldck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobielldck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(u + v, k) = (JacobiNC(u, k)*JacobiNC(v, k)+ JacobiSC(u, k)*JacobiDC(u, k)*JacobiSC(v, k)*JacobiDC(v, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[u + v, (k)^2] == Divide[JacobiNC[u, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[u, (k)^2]*JacobiDC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiDC[v, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.356171111+.335718656*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3210452605+.1984107752*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.356171110076661, 0.3357186535359711]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.3210452604978905, 0.19841077324251138]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E9 22.8.E9] || [[Item:Q6974|<math>\Jacobiellsck@@{(u+v)}{k} = \frac{\Jacobiellsck@@{u}{k}\Jacobielldck@@{v}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{v}{k}\Jacobielldck@@{u}{k}\Jacobiellnck@@{u}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(u + v, k) = (JacobiSC(u, k)*JacobiDC(v, k)*JacobiNC(v, k)+ JacobiSC(v, k)*JacobiDC(u, k)*JacobiNC(u, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[u + v, (k)^2] == Divide[JacobiSC[u, (k)^2]*JacobiDC[v, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[v, (k)^2]*JacobiDC[u, (k)^2]*JacobiNC[u, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.370082581+.423198902*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2742031773e-1-2.068263955*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 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 [270 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3700825790735573, 0.42319889849983916]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.027420317388659004, -2.068263954207401]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E10 22.8.E10] || [[Item:Q6975|<math>\Jacobiellnsk@@{(u+v)}{k} = \frac{\Jacobiellnsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{v}{k}-\Jacobiellnsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(u + v, k) = (JacobiNS(u, k)*JacobiDS(v, k)*JacobiCS(v, k)- JacobiNS(v, k)*JacobiDS(u, k)*JacobiCS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[u + v, (k)^2] == Divide[JacobiNS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiCS[v, (k)^2]- JacobiNS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiCS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E11 22.8.E11] || [[Item:Q6976|<math>\Jacobielldsk@@{(u+v)}{k} = \frac{\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(u + v, k) = (JacobiDS(u, k)*JacobiCS(v, k)*JacobiNS(v, k)- JacobiDS(v, k)*JacobiCS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[u + v, (k)^2] == Divide[JacobiDS[u, (k)^2]*JacobiCS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiDS[v, (k)^2]*JacobiCS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E12 22.8.E12] || [[Item:Q6977|<math>\Jacobiellcsk@@{(u+v)}{k} = \frac{\Jacobiellcsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobiellcsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(u + v, k) = (JacobiCS(u, k)*JacobiDS(v, k)*JacobiNS(v, k)- JacobiCS(v, k)*JacobiDS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[u + v, (k)^2] == Divide[JacobiCS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiCS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E13 22.8.E13] || [[Item:Q6978|<math>\Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(u + v, k) = ((JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[u + v, (k)^2] == Divide[(JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2),JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E14 22.8.E14] || [[Item:Q6979|<math>\Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(u + v, k) = (JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/22.8.E15 22.8.E15] || [[Item:Q6980|<math>\Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(u + v, k) = (JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E16 22.8.E16] || [[Item:Q6981|<math>\Jacobiellcnk@@{(u+v)}{k} = \frac{1-\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}+k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(u + v, k) = (1 - (JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2)+ (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[u + v, (k)^2] == Divide[1 - (JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2)+ (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2),JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/22.8.E17 22.8.E17] || [[Item:Q6982|<math>\Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(u + v, k) = (JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(u, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(v, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]]</syntaxhighlight> || Successful || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E18 22.8.E18] || [[Item:Q6983|<math>\Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsnk@@{u}{k}\Jacobiellsnk@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(u + v, k) = (JacobiCN(u, k)*JacobiDN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+1 - (k)^(2)*JacobiSN(u, k)*JacobiSN(v, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[u + v, (k)^2] == Divide[JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+1 - (k)^(2)*JacobiSN[u, (k)^2]*JacobiSN[v, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6011182715+.1479228534*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.889107517+1.386528377*I
Test Values: {u = 1/2*3^(1/2)+1/2*I, v = 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[-0.6011182715762831, 0.14792285354183748]
Test Values: {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.8891075280231666, 1.3865283695917823]
Test Values: {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E19 22.8.E19] || [[Item:Q6984|<math>z_{1}+z_{2}+z_{3}+z_{4} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[1]+ z[2]+ z[3]+ z[4] = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 1]+ Subscript[z, 2]+ Subscript[z, 3]+ Subscript[z, 4] == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.8.E21 22.8.E21] || [[Item:Q6986|<math>{k^{\prime}}^{2}-{k^{\prime}}^{2}k^{2}\Jacobiellsnk@@{z_{1}}{k}\Jacobiellsnk@@{z_{2}}{k}\Jacobiellsnk@@{z_{3}}{k}\Jacobiellsnk@@{z_{4}}{k}+k^{2}\Jacobiellcnk@@{z_{1}}{k}\Jacobiellcnk@@{z_{2}}{k}\Jacobiellcnk@@{z_{3}}{k}\Jacobiellcnk@@{z_{4}}{k}-\Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{3}}{k}\Jacobielldnk@@{z_{4}}{k} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>1 - (k)^(2)-1 - (k)^(2)*(k)^(2)* JacobiSN(z[1], k)*JacobiSN(z[2], k)*JacobiSN(z[3], k)*JacobiSN(z[4], k)+ (k)^(2)* JacobiCN(z[1], k)*JacobiCN(z[2], k)*JacobiCN(z[3], k)*JacobiCN(z[4], k)- JacobiDN(z[1], k)*JacobiDN(z[2], k)*JacobiDN(z[3], k)*JacobiDN(z[4], k) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 - (k)^(2)-1 - (k)^(2)*(k)^(2)* JacobiSN[Subscript[z, 1], (k)^2]*JacobiSN[Subscript[z, 2], (k)^2]*JacobiSN[Subscript[z, 3], (k)^2]*JacobiSN[Subscript[z, 4], (k)^2]+ (k)^(2)* JacobiCN[Subscript[z, 1], (k)^2]*JacobiCN[Subscript[z, 2], (k)^2]*JacobiCN[Subscript[z, 3], (k)^2]*JacobiCN[Subscript[z, 4], (k)^2]- JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.174291399-.4389390377*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.960363418+.5505072293*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 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 [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.0
Test Values: {Rule[k, 2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -8.0
Test Values: {Rule[k, 3]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/22.8.E22 22.8.E22] || [[Item:Q6987|<math>z_{1}+z_{2}+z_{3}+z_{4} = 2\compellintKk@{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[1]+ z[2]+ z[3]+ z[4] = 2*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 1]+ Subscript[z, 2]+ Subscript[z, 3]+ Subscript[z, 4] == 2*EllipticK[(k)^2]</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[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.7783512603251586, 4.156515647499643]
Test Values: {Rule[k, 2], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E24 22.8.E24] || [[Item:Q6989|<math>z_{1}-z_{2} = z_{2}-z_{3}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[1]- z[2] = z[2]- z[3]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 1]- Subscript[z, 2] == Subscript[z, 2]- Subscript[z, 3]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.366025404+.3660254040*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3660254040-1.366025404*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.3660254037844384, 0.36602540378443876]
Test Values: {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3660254037844386, -1.3660254037844386]
Test Values: {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E24 22.8.E24] || [[Item:Q6989|<math>z_{2}-z_{3} = \tfrac{2}{3}\compellintKk@{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[2]- z[3] = (2)/(3)*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 2]- Subscript[z, 3] == Divide[2,3]*EllipticK[(k)^2]</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[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.561916784937532, 0.7188385491665478]
Test Values: {Rule[k, 2], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E26 22.8.E26] || [[Item:Q6991|<math>z_{1}-z_{2} = z_{2}-z_{3}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[1]- z[2] = z[2]- z[3]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 1]- Subscript[z, 2] == Subscript[z, 2]- Subscript[z, 3]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.366025404+.3660254040*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3660254040-1.366025404*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.3660254037844384, 0.36602540378443876]
Test Values: {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3660254037844386, -1.3660254037844386]
Test Values: {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E26 22.8.E26] || [[Item:Q6991|<math>z_{2}-z_{3} = z_{3}-z_{4}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[2]- z[3] = z[3]- z[4]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 2]- Subscript[z, 3] == Subscript[z, 3]- Subscript[z, 4]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.366025404+.3660254040*I
Test Values: {z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3660254040-1.366025404*I
Test Values: {z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 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 [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.3660254037844384, 0.36602540378443876]
Test Values: {Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.3660254037844386, -1.3660254037844386]
Test Values: {Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E26 22.8.E26] || [[Item:Q6991|<math>z_{3}-z_{4} = \tfrac{1}{2}\compellintKk@{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>z[3]- z[4] = (1)/(2)*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[z, 3]- Subscript[z, 4] == Divide[1,2]*EllipticK[(k)^2]</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[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.42143758870314907, 0.5391289118749109]
Test Values: {Rule[k, 2], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E27 22.8.E27] || [[Item:Q6992|<math>\Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{3}}{k} = \Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z[1], k)*JacobiDN(z[3], k) = JacobiDN(z[2], k)*JacobiDN(z[4], k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2] == JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.4756423320-.5071574760*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2), k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.554390475+.7152903744*I
Test Values: {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2), k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.475642332072964, -0.5071574758549496]
Test Values: {Rule[k, 1], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.5543904750381285, 0.715290373196519]
Test Values: {Rule[k, 2], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.8.E27 22.8.E27] || [[Item:Q6992|<math>\Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k} = k^{\prime}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z[2], k)*JacobiDN(z[4], k) = sqrt(1 - (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] == Sqrt[1 - (k)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4314194118-.3859954480*I
Test Values: {z[2] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8474767071-1.646914265*I
Test Values: {z[2] = 1/2*3^(1/2)+1/2*I, z[4] = 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[0.4314194120331003, -0.3859954480737353]
Test Values: {Rule[k, 1], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.8474767070969642, -1.6469142655565594]
Test Values: {Rule[k, 2], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E1 22.9.E1] || [[Item:Q6993|<math>s_{m,p}^{(2)} = \Jacobiellsnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[m , p])^(2) = JacobiSN(z + 2*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, m , p])^(2) == JacobiSN[z + 2*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E2 22.9.E2] || [[Item:Q6994|<math>c_{m,p}^{(2)} = \Jacobiellcnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[m , p])^(2) = JacobiCN(z + 2*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, m , p])^(2) == JacobiCN[z + 2*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E3 22.9.E3] || [[Item:Q6995|<math>d_{m,p}^{(2)} = \Jacobielldnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(d[m , p])^(2) = JacobiDN(z + 2*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[d, m , p])^(2) == JacobiDN[z + 2*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E4 22.9.E4] || [[Item:Q6996|<math>s_{m,p}^{(4)} = \Jacobiellsnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[m , p])^(4) = JacobiSN(z + 4*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, m , p])^(4) == JacobiSN[z + 4*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E5 22.9.E5] || [[Item:Q6997|<math>c_{m,p}^{(4)} = \Jacobiellcnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[m , p])^(4) = JacobiCN(z + 4*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, m , p])^(4) == JacobiCN[z + 4*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E6 22.9.E6] || [[Item:Q6998|<math>d_{m,p}^{(4)} = \Jacobielldnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(d[m , p])^(4) = JacobiDN(z + 4*(p)^(- 1)*(m - 1)*EllipticK(k), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[d, m , p])^(4) == JacobiDN[z + 4*(p)^(- 1)*(m - 1)*EllipticK[(k)^2], (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.9.E8 22.9.E8] || [[Item:Q7000|<math>s_{1,3}^{(4)}s_{2,3}^{(4)}+s_{2,3}^{(4)}s_{3,3}^{(4)}+s_{3,3}^{(4)}s_{1,3}^{(4)} = \frac{\kappa^{2}-1}{k^{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[1 , 3])^(4)*(s[2 , 3])^(4)+ (s[2 , 3])^(4)*(s[3 , 3])^(4)+ (s[3 , 3])^(4)*(s[1 , 3])^(4) = ((JacobiDN(2*EllipticK(k)/3, k))^(2)- 1)/((k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, 1 , 3])^(4)*(Subscript[s, 2 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[s, 3 , 3])^(4)+ (Subscript[s, 3 , 3])^(4)*(Subscript[s, 1 , 3])^(4) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)- 1,(k)^(2)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E9 22.9.E9] || [[Item:Q7001|<math>c_{1,3}^{(4)}c_{2,3}^{(4)}+c_{2,3}^{(4)}c_{3,3}^{(4)}+c_{3,3}^{(4)}c_{1,3}^{(4)} = -\frac{\kappa(\kappa+2)}{(1+\kappa)^{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[1 , 3])^(4)*(c[2 , 3])^(4)+ (c[2 , 3])^(4)*(c[3 , 3])^(4)+ (c[3 , 3])^(4)*(c[1 , 3])^(4) = -((JacobiDN(2*EllipticK(k)/3, k))*((JacobiDN(2*EllipticK(k)/3, k))+ 2))/((1 +(JacobiDN(2*EllipticK(k)/3, k)))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)+ (Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4) == -Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])*((JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])+ 2),(1 +(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2]))^(2)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E10 22.9.E10] || [[Item:Q7002|<math>d_{1,3}^{(2)}d_{2,3}^{(2)}+d_{2,3}^{(2)}d_{3,3}^{(2)}+d_{3,3}^{(2)}d_{1,3}^{(2)} = d_{1,3}^{(4)}d_{2,3}^{(4)}+d_{2,3}^{(4)}d_{3,3}^{(4)}+d_{3,3}^{(4)}d_{1,3}^{(4)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(d[1 , 3])^(2)*(d[2 , 3])^(2)+ (d[2 , 3])^(2)*(d[3 , 3])^(2)+ (d[3 , 3])^(2)*(d[1 , 3])^(2) = (d[1 , 3])^(4)*(d[2 , 3])^(4)+ (d[2 , 3])^(4)*(d[3 , 3])^(4)+ (d[3 , 3])^(4)*(d[1 , 3])^(4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[d, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)+ (Subscript[d, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)+ (Subscript[d, 3 , 3])^(2)*(Subscript[d, 1 , 3])^(2) == (Subscript[d, 1 , 3])^(4)*(Subscript[d, 2 , 3])^(4)+ (Subscript[d, 2 , 3])^(4)*(Subscript[d, 3 , 3])^(4)+ (Subscript[d, 3 , 3])^(4)*(Subscript[d, 1 , 3])^(4)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E11 22.9.E11] || [[Item:Q7003|<math>\left(d_{1,2}^{(2)}\right)^{2}d_{2,2}^{(2)}+\left(d_{2,2}^{(2)}\right)^{2}d_{1,2}^{(2)} = k^{\prime}\left(d_{1,2}^{(2)}+ d_{2,2}^{(2)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((d[1 , 2])^(2))^(2)* (d[2 , 2])^(2)+((d[2 , 2])^(2))^(2)* (d[1 , 2])^(2) = sqrt(1 - (k)^(2))*((d[1 , 2])^(2)+ (d[2 , 2])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[d, 1 , 2])^(2))^(2)* (Subscript[d, 2 , 2])^(2)+((Subscript[d, 2 , 2])^(2))^(2)* (Subscript[d, 1 , 2])^(2) == Sqrt[1 - (k)^(2)]*((Subscript[d, 1 , 2])^(2)+ (Subscript[d, 2 , 2])^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E12 22.9.E12] || [[Item:Q7004|<math>c_{1,2}^{(2)}s_{1,2}^{(2)}d_{2,2}^{(2)}+c_{2,2}^{(2)}s_{2,2}^{(2)}d_{1,2}^{(2)} = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[1 , 2])^(2)*(s[1 , 2])^(2)*(d[2 , 2])^(2)+ (c[2 , 2])^(2)*(s[2 , 2])^(2)*(d[1 , 2])^(2) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, 1 , 2])^(2)*(Subscript[s, 1 , 2])^(2)*(Subscript[d, 2 , 2])^(2)+ (Subscript[c, 2 , 2])^(2)*(Subscript[s, 2 , 2])^(2)*(Subscript[d, 1 , 2])^(2) == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E13 22.9.E13] || [[Item:Q7005|<math>s_{1,3}^{(4)}s_{2,3}^{(4)}s_{3,3}^{(4)} = -\frac{1}{1-\kappa^{2}}\left(s_{1,3}^{(4)}+s_{2,3}^{(4)}+s_{3,3}^{(4)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[1 , 3])^(4)*(s[2 , 3])^(4)*(s[3 , 3])^(4) = -(1)/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((s[1 , 3])^(4)+ (s[2 , 3])^(4)+ (s[3 , 3])^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, 1 , 3])^(4)*(Subscript[s, 2 , 3])^(4)*(Subscript[s, 3 , 3])^(4) == -Divide[1,1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[s, 1 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)+ (Subscript[s, 3 , 3])^(4))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E14 22.9.E14] || [[Item:Q7006|<math>c_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)} = \frac{\kappa^{2}}{1-\kappa^{2}}\left(c_{1,3}^{(4)}+c_{2,3}^{(4)}+c_{3,3}^{(4)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[1 , 3])^(4)*(c[2 , 3])^(4)*(c[3 , 3])^(4) = ((JacobiDN(2*EllipticK(k)/3, k))^(2))/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((c[1 , 3])^(4)+ (c[2 , 3])^(4)+ (c[3 , 3])^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2),1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[c, 1 , 3])^(4)+ (Subscript[c, 2 , 3])^(4)+ (Subscript[c, 3 , 3])^(4))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E15 22.9.E15] || [[Item:Q7007|<math>d_{1,3}^{(2)}d_{2,3}^{(2)}d_{3,3}^{(2)} = \frac{\kappa^{2}+k^{2}-1}{1-\kappa^{2}}\left(d_{1,3}^{(2)}+d_{2,3}^{(2)}+d_{3,3}^{(2)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(d[1 , 3])^(2)*(d[2 , 3])^(2)*(d[3 , 3])^(2) = ((JacobiDN(2*EllipticK(k)/3, k))^(2)+ (k)^(2)- 1)/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((d[1 , 3])^(2)+ (d[2 , 3])^(2)+ (d[3 , 3])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[d, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)+ (k)^(2)- 1,1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[d, 1 , 3])^(2)+ (Subscript[d, 2 , 3])^(2)+ (Subscript[d, 3 , 3])^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E16 22.9.E16] || [[Item:Q7008|<math>s_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)}+s_{2,3}^{(4)}c_{3,3}^{(4)}c_{1,3}^{(4)}+s_{3,3}^{(4)}c_{1,3}^{(4)}c_{2,3}^{(4)} = \frac{\kappa(\kappa+2)}{1-\kappa^{2}}\left(s_{1,3}^{(4)}+s_{2,3}^{(4)}+s_{3,3}^{(4)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[1 , 3])^(4)*(c[2 , 3])^(4)*(c[3 , 3])^(4)+ (s[2 , 3])^(4)*(c[3 , 3])^(4)*(c[1 , 3])^(4)+ (s[3 , 3])^(4)*(c[1 , 3])^(4)*(c[2 , 3])^(4) = ((JacobiDN(2*EllipticK(k)/3, k))*((JacobiDN(2*EllipticK(k)/3, k))+ 2))/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((s[1 , 3])^(4)+ (s[2 , 3])^(4)+ (s[3 , 3])^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)+ (Subscript[s, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])*((JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])+ 2),1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[s, 1 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)+ (Subscript[s, 3 , 3])^(4))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E17 22.9.E17] || [[Item:Q7009|<math>d_{1,4}^{(2)}d_{2,4}^{(2)}d_{3,4}^{(2)}+ d_{2,4}^{(2)}d_{3,4}^{(2)}d_{4,4}^{(2)}+d_{3,4}^{(2)}d_{4,4}^{(2)}d_{1,4}^{(2)}+ d_{4,4}^{(2)}d_{1,4}^{(2)}d_{2,4}^{(2)} = k^{\prime}{\left(+ d_{1,4}^{(2)}+d_{2,4}^{(2)}+ d_{3,4}^{(2)}+d_{4,4}^{(2)}\right)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(d[1 , 4])^(2)*(d[2 , 4])^(2)*(d[3 , 4])^(2)+ (d[2 , 4])^(2)*(d[3 , 4])^(2)*(d[4 , 4])^(2)+ (d[3 , 4])^(2)*(d[4 , 4])^(2)*(d[1 , 4])^(2)+ (d[4 , 4])^(2)*(d[1 , 4])^(2)*(d[2 , 4])^(2) = sqrt(1 - (k)^(2))*(+ (d[1 , 4])^(2)+ (d[2 , 4])^(2)+ (d[3 , 4])^(2)+ (d[4 , 4])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[d, 1 , 4])^(2)*(Subscript[d, 2 , 4])^(2)*(Subscript[d, 3 , 4])^(2)+ (Subscript[d, 2 , 4])^(2)*(Subscript[d, 3 , 4])^(2)*(Subscript[d, 4 , 4])^(2)+ (Subscript[d, 3 , 4])^(2)*(Subscript[d, 4 , 4])^(2)*(Subscript[d, 1 , 4])^(2)+ (Subscript[d, 4 , 4])^(2)*(Subscript[d, 1 , 4])^(2)*(Subscript[d, 2 , 4])^(2) == Sqrt[1 - (k)^(2)]*(+ (Subscript[d, 1 , 4])^(2)+ (Subscript[d, 2 , 4])^(2)+ (Subscript[d, 3 , 4])^(2)+ (Subscript[d, 4 , 4])^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E18 22.9.E18] || [[Item:Q7010|<math>\left(d_{1,4}^{(2)}\right)^{2}d_{3,4}^{(2)}+\left(d_{2,4}^{(2)}\right)^{2}d_{4,4}^{(2)}+\left(d_{3,4}^{(2)}\right)^{2}d_{1,4}^{(2)}+\left(d_{4,4}^{(2)}\right)^{2}d_{2,4}^{(2)} = k^{\prime}{\left(d_{1,4}^{(2)}+ d_{2,4}^{(2)}+d_{3,4}^{(2)}+ d_{4,4}^{(2)}\right)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((d[1 , 4])^(2))^(2)* (d[3 , 4])^(2)+((d[2 , 4])^(2))^(2)* (d[4 , 4])^(2)+((d[3 , 4])^(2))^(2)* (d[1 , 4])^(2)+((d[4 , 4])^(2))^(2)* (d[2 , 4])^(2) = sqrt(1 - (k)^(2))*((d[1 , 4])^(2)+ (d[2 , 4])^(2)+ (d[3 , 4])^(2)+ (d[4 , 4])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[d, 1 , 4])^(2))^(2)* (Subscript[d, 3 , 4])^(2)+((Subscript[d, 2 , 4])^(2))^(2)* (Subscript[d, 4 , 4])^(2)+((Subscript[d, 3 , 4])^(2))^(2)* (Subscript[d, 1 , 4])^(2)+((Subscript[d, 4 , 4])^(2))^(2)* (Subscript[d, 2 , 4])^(2) == Sqrt[1 - (k)^(2)]*((Subscript[d, 1 , 4])^(2)+ (Subscript[d, 2 , 4])^(2)+ (Subscript[d, 3 , 4])^(2)+ (Subscript[d, 4 , 4])^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E19 22.9.E19] || [[Item:Q7011|<math>c_{1,4}^{(2)}s_{1,4}^{(2)}d_{3,4}^{(2)}+c_{3,4}^{(2)}s_{3,4}^{(2)}d_{1,4}^{(2)} = c_{2,4}^{(2)}s_{2,4}^{(2)}d_{4,4}^{(2)}+c_{4,4}^{(2)}s_{4,4}^{(2)}d_{2,4}^{(2)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(c[1 , 4])^(2)*(s[1 , 4])^(2)*(d[3 , 4])^(2)+ (c[3 , 4])^(2)*(s[3 , 4])^(2)*(d[1 , 4])^(2) = (c[2 , 4])^(2)*(s[2 , 4])^(2)*(d[4 , 4])^(2)+ (c[4 , 4])^(2)*(s[4 , 4])^(2)*(d[2 , 4])^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[c, 1 , 4])^(2)*(Subscript[s, 1 , 4])^(2)*(Subscript[d, 3 , 4])^(2)+ (Subscript[c, 3 , 4])^(2)*(Subscript[s, 3 , 4])^(2)*(Subscript[d, 1 , 4])^(2) == (Subscript[c, 2 , 4])^(2)*(Subscript[s, 2 , 4])^(2)*(Subscript[d, 4 , 4])^(2)+ (Subscript[c, 4 , 4])^(2)*(Subscript[s, 4 , 4])^(2)*(Subscript[d, 2 , 4])^(2)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E20 22.9.E20] || [[Item:Q7012|<math>\left(d_{1,2}^{(2)}\right)^{3}d_{2,2}^{(2)}+\left(d_{2,2}^{(2)}\right)^{3}d_{1,2}^{(2)} = k^{\prime}\left(\left(d_{1,2}^{(2)}\right)^{2}+\left(d_{2,2}^{(2)}\right)^{2}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((d[1 , 2])^(2))^(3)* (d[2 , 2])^(2)+((d[2 , 2])^(2))^(3)* (d[1 , 2])^(2) = sqrt(1 - (k)^(2))*(((d[1 , 2])^(2))^(2)+((d[2 , 2])^(2))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>((Subscript[d, 1 , 2])^(2))^(3)* (Subscript[d, 2 , 2])^(2)+((Subscript[d, 2 , 2])^(2))^(3)* (Subscript[d, 1 , 2])^(2) == Sqrt[1 - (k)^(2)]*(((Subscript[d, 1 , 2])^(2))^(2)+((Subscript[d, 2 , 2])^(2))^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E21 22.9.E21] || [[Item:Q7013|<math>k^{2}c_{1,2}^{(2)}s_{1,2}^{(2)}c_{2,2}^{(2)}s_{2,2}^{(2)} = k^{\prime}\left(1-\left(s_{1,2}^{(2)}\right)^{2}-\left(s_{2,2}^{(2)}\right)^{2}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)* (c[1 , 2])^(2)*(s[1 , 2])^(2)*(c[2 , 2])^(2)*(s[2 , 2])^(2) = sqrt(1 - (k)^(2))*(1 -((s[1 , 2])^(2))^(2)-((s[2 , 2])^(2))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)* (Subscript[c, 1 , 2])^(2)*(Subscript[s, 1 , 2])^(2)*(Subscript[c, 2 , 2])^(2)*(Subscript[s, 2 , 2])^(2) == Sqrt[1 - (k)^(2)]*(1 -((Subscript[s, 1 , 2])^(2))^(2)-((Subscript[s, 2 , 2])^(2))^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E22 22.9.E22] || [[Item:Q7014|<math>s_{1,3}^{(2)}c_{1,3}^{(2)}d_{2,3}^{(2)}d_{3,3}^{(2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}d_{3,3}^{(2)}d_{1,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^{(2)}d_{1,3}^{(2)}d_{2,3}^{(2)} = \frac{\kappa^{2}+k^{2}-1}{1-\kappa^{2}}\left(s_{1,3}^{(2)}c_{1,3}^{(2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^{(2)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[1 , 3])^(2)*(c[1 , 3])^(2)*(d[2 , 3])^(2)*(d[3 , 3])^(2)+ (s[2 , 3])^(2)*(c[2 , 3])^(2)*(d[3 , 3])^(2)*(d[1 , 3])^(2)+ (s[3 , 3])^(2)*(c[3 , 3])^(2)*(d[1 , 3])^(2)*(d[2 , 3])^(2) = ((JacobiDN(2*EllipticK(k)/3, k))^(2)+ (k)^(2)- 1)/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((s[1 , 3])^(2)*(c[1 , 3])^(2)+ (s[2 , 3])^(2)*(c[2 , 3])^(2)+ (s[3 , 3])^(2)*(c[3 , 3])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, 1 , 3])^(2)*(Subscript[c, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)+ (Subscript[s, 2 , 3])^(2)*(Subscript[c, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)*(Subscript[d, 1 , 3])^(2)+ (Subscript[s, 3 , 3])^(2)*(Subscript[c, 3 , 3])^(2)*(Subscript[d, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)+ (k)^(2)- 1,1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[s, 1 , 3])^(2)*(Subscript[c, 1 , 3])^(2)+ (Subscript[s, 2 , 3])^(2)*(Subscript[c, 2 , 3])^(2)+ (Subscript[s, 3 , 3])^(2)*(Subscript[c, 3 , 3])^(2))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.9.E23 22.9.E23] || [[Item:Q7015|<math>s_{1,3}^{(4)}d_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}c_{3,3}^{(4)}c_{1,3}^{(4)}+s_{3,3}^{(4)}d_{3,3}^{(4)}c_{1,3}^{(4)}c_{2,3}^{(4)} = \frac{\kappa^{2}}{1-\kappa^{2}}\left(s_{1,3}^{(4)}d_{1,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(s[1 , 3])^(4)*(d[1 , 3])^(4)*(c[2 , 3])^(4)*(c[3 , 3])^(4)+ (s[2 , 3])^(4)*(d[2 , 3])^(4)*(c[3 , 3])^(4)*(c[1 , 3])^(4)+ (s[3 , 3])^(4)*(d[3 , 3])^(4)*(c[1 , 3])^(4)*(c[2 , 3])^(4) = ((JacobiDN(2*EllipticK(k)/3, k))^(2))/(1 -(JacobiDN(2*EllipticK(k)/3, k))^(2))*((s[1 , 3])^(4)*(d[1 , 3])^(4)+ (s[2 , 3])^(4)*(d[2 , 3])^(4)+ (s[2 , 3])^(4)*(d[2 , 3])^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Subscript[s, 1 , 3])^(4)*(Subscript[d, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[d, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)+ (Subscript[s, 3 , 3])^(4)*(Subscript[d, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4) == Divide[(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2),1 -(JacobiDN[2*EllipticK[(k)^2]/3, (k)^2])^(2)]*((Subscript[s, 1 , 3])^(4)*(Subscript[d, 1 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[d, 2 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[d, 2 , 3])^(4))</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/22.11.E1 22.11.E1] || [[Item:Q7025|<math>\Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.11.E2 22.11.E2] || [[Item:Q7026|<math>\Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, k) = (2*Pi)/(K*k)*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.11.E3 22.11.E3] || [[Item:Q7027|<math>\Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, k) = (Pi)/(2*EllipticK(k))+(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]]+Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.11.E4 22.11.E4] || [[Item:Q7028|<math>\Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(z, k) = (2*Pi)/(K*k)*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.11.E5 22.11.E5] || [[Item:Q7029|<math>\Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(z, k) = (2*Pi)/(K*k*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n +(1)/(2))* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[z, (k)^2] == Divide[2*Pi,K*k*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n +Divide[1,2])* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E6 22.11.E6] || [[Item:Q7030|<math>\Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(z, k) = (Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))+(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* cos(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]+Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Cos[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E7 22.11.E7] || [[Item:Q7031|<math>\Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = (2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E8 22.11.E8] || [[Item:Q7032|<math>\Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* sin((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Sin[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E9 22.11.E9] || [[Item:Q7033|<math>\Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(z, k)-(Pi)/(2*EllipticK(k))*cot(zeta) = -(2*Pi)/(EllipticK(k))*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Cot[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E10 22.11.E10] || [[Item:Q7034|<math>\Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(z, k)-(Pi)/(2*EllipticK(k))*sec(zeta) = (2*Pi)/(EllipticK(k))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Sec[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E11 22.11.E11] || [[Item:Q7035|<math>\Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*sec(zeta) = -(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)* cos((2*n + 1)*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n + 1)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sec[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)* Cos[(2*n + 1)*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E12 22.11.E12] || [[Item:Q7036|<math>\Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*tan(zeta) = (2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)*(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)* sin(2*n*zeta))/(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n)), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Tan[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)*(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)* Sin[2*n*\[Zeta]],1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.11.E13 22.11.E13] || [[Item:Q7037|<math>\Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2) = (1)/((k)^(2))*(1 -(EllipticE(k))/(EllipticK(k)))-(2*(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))*sum((n*(q)^(n))/(1 -(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n))*cos(2*n*zeta), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2) == Divide[1,(k)^(2)]*(1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2*(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]*Sum[Divide[n*(q)^(n),1 -(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n)]*Cos[2*n*\[Zeta]], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.12.E1 22.12.E1] || [[Item:Q7039|<math>\tau = i\ccompellintKk@{k}/\compellintKk@{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>tau = I*EllipticCK(k)/EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Tau] == I*EllipticK[1-(k)^2]/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: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[k, 1], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.4867361401447923, 0.0147898206680519]
Test Values: {Rule[k, 2], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.12.E2 22.12.E2] || [[Item:Q7040|<math>2Kk\Jacobiellsnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*K*k*JacobiSN(2*K*t, k) = sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*K*k*JacobiSN[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E2 22.12.E2] || [[Item:Q7040|<math>\sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t - m -(n +(1)/(2))*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t - m -(n +Divide[1,2])*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E3 22.12.E3] || [[Item:Q7041|<math>2iKk\Jacobiellcnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*I*K*k*JacobiCN(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*I*K*k*JacobiCN[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E3 22.12.E3] || [[Item:Q7041|<math>\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t - m -(n +(1)/(2))*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t - m -(n +Divide[1,2])*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E4 22.12.E4] || [[Item:Q7042|<math>2iK\Jacobielldnk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*I*EllipticK(k)*JacobiDN(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t -(n +(1)/(2))*tau))), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*I*EllipticK[(k)^2]*JacobiDN[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E4 22.12.E4] || [[Item:Q7042|<math>\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-(n+\frac{1}{2})\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t -(n +(1)/(2))*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t - m -(n +(1)/(2))*tau), m = - M..M), M = infinity)), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t - m -(n +Divide[1,2])*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E5 22.12.E5] || [[Item:Q7043|<math>2Kk\Jacobiellcdk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*K*k*JacobiCD(2*K*t, k) = sum((Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*K*k*JacobiCD[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E5 22.12.E5] || [[Item:Q7043|<math>\sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t +(1)/(2)- m -(n +(1)/(2))*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t +Divide[1,2]- m -(n +Divide[1,2])*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E6 22.12.E6] || [[Item:Q7044|<math>-2iKkk^{\prime}\Jacobiellsdk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>- 2*I*K*k*sqrt(1 - (k)^(2))*JacobiSD(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- 2*I*K*k*Sqrt[1 - (k)^(2)]*JacobiSD[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E6 22.12.E6] || [[Item:Q7044|<math>\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t +(1)/(2)- m -(n +(1)/(2))*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t +Divide[1,2]- m -(n +Divide[1,2])*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E7 22.12.E7] || [[Item:Q7045|<math>2iKk^{\prime}\Jacobiellndk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*I*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiND(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*I*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiND[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E7 22.12.E7] || [[Item:Q7045|<math>\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\lim_{M\to\infty}\left(\sum_{m=-M}^{M}\frac{1}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)* limit(sum((1)/(t +(1)/(2)- m -(n +(1)/(2))*tau), m = - M..M), M = infinity), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)* Limit[Sum[Divide[1,t +Divide[1,2]- m -(n +Divide[1,2])*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E8 22.12.E8] || [[Item:Q7046|<math>2K\Jacobielldck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*EllipticK(k)*JacobiDC(2*K*t, k) = sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*EllipticK[(k)^2]*JacobiDC[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/22.12.E8 22.12.E8] || [[Item:Q7046|<math>\sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t+\frac{1}{2}-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E9 22.12.E9] || [[Item:Q7047|<math>2Kk^{\prime}\Jacobiellnck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiNC(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiNC[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E9 22.12.E9] || [[Item:Q7047|<math>\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E10 22.12.E10] || [[Item:Q7048|<math>-2Kk^{\prime}\Jacobiellsck@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>- 2*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiSC(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)- n*tau))), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- 2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiSC[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E10 22.12.E10] || [[Item:Q7048|<math>\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-n\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t+\frac{1}{2}-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)- n*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t +(1)/(2)- m - n*tau), m = - M..M), M = infinity)), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t +Divide[1,2]- m - n*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E11 22.12.E11] || [[Item:Q7049|<math>2K\Jacobiellnsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*EllipticK(k)*JacobiNS(2*K*t, k) = sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*EllipticK[(k)^2]*JacobiNS[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E11 22.12.E11] || [[Item:Q7049|<math>\sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t - m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || Skip - symbolical successful subtest || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E12 22.12.E12] || [[Item:Q7050|<math>2K\Jacobielldsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*EllipticK(k)*JacobiDS(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*EllipticK[(k)^2]*JacobiDS[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E12 22.12.E12] || [[Item:Q7050|<math>\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t - m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None]</syntaxhighlight> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E13 22.12.E13] || [[Item:Q7051|<math>2K\Jacobiellcsk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-n\tau)}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>2*EllipticK(k)*JacobiCS(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t - n*tau))), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*EllipticK[(k)^2]*JacobiCS[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t - n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.12.E13 22.12.E13] || [[Item:Q7051|<math>\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-n\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t-m-n\tau}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t - n*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t - m - n*tau), m = - M..M), M = infinity)), n = - N..N), N = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t - n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t - m - n*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.13.E1 22.13.E1] || [[Item:Q7052|<math>\left(\deriv{}{z}\Jacobiellsnk@{z}{k}\right)^{2} = \left(1-\Jacobiellsnk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellsnk^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiSN(z, k), z))^(2) = (1 - (JacobiSN(z, k))^(2))*(1 - (k)^(2)* (JacobiSN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiSN[z, (k)^2], z])^(2) == (1 - (JacobiSN[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiSN[z, (k)^2])^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E2 22.13.E2] || [[Item:Q7053|<math>\left(\deriv{}{z}\Jacobiellcnk@{z}{k}\right)^{2} = {\left(1-\Jacobiellcnk^{2}@{z}{k}\right)}{\left({k^{\prime}}^{2}+k^{2}\Jacobiellcnk^{2}@{z}{k}\right)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiCN(z, k), z))^(2) = (1 - (JacobiCN(z, k))^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiCN[z, (k)^2], z])^(2) == (1 - (JacobiCN[z, (k)^2])^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN[z, (k)^2])^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E3 22.13.E3] || [[Item:Q7054|<math>\left(\deriv{}{z}\Jacobielldnk@{z}{k}\right)^{2} = \left(1-\Jacobielldnk^{2}@{z}{k}\right)\left(\Jacobielldnk^{2}@{z}{k}-{k^{\prime}}^{2}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiDN(z, k), z))^(2) = (1 - (JacobiDN(z, k))^(2))*((JacobiDN(z, k))^(2)-1 - (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiDN[z, (k)^2], z])^(2) == (1 - (JacobiDN[z, (k)^2])^(2))*((JacobiDN[z, (k)^2])^(2)-1 - (k)^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.137161176+.7719908960*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 14.77981366-.6810923425*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.1371611759337996, 0.7719908961474706]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[14.779813656775712, -0.6810923360985438]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E4 22.13.E4] || [[Item:Q7055|<math>\left(\deriv{}{z}\Jacobiellcdk@{z}{k}\right)^{2} = \left(1-\Jacobiellcdk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellcdk^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiCD(z, k), z))^(2) = (1 - (JacobiCD(z, k))^(2))*(1 - (k)^(2)* (JacobiCD(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiCD[z, (k)^2], z])^(2) == (1 - (JacobiCD[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiCD[z, (k)^2])^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E5 22.13.E5] || [[Item:Q7056|<math>\left(\deriv{}{z}\Jacobiellsdk@{z}{k}\right)^{2} = {\left(1-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\right)}{\left(1+k^{2}\Jacobiellsdk^{2}@{z}{k}\right)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiSD(z, k), z))^(2) = (1 -1 - (k)^(2)*(JacobiSD(z, k))^(2))*(1 + (k)^(2)* (JacobiSD(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiSD[z, (k)^2], z])^(2) == (1 -1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2))*(1 + (k)^(2)* (JacobiSD[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3306277626+2.965675443*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.240181814+.5678364413*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.33062776288262774, 2.9656754410633357]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.24018181473062, 0.5678364360004244]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E6 22.13.E6] || [[Item:Q7057|<math>\left(\deriv{}{z}\Jacobiellndk@{z}{k}\right)^{2} = \left(\Jacobiellndk^{2}@{z}{k}-1\right)\left(1-{k^{\prime}}^{2}\Jacobiellndk^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiND(z, k), z))^(2) = ((JacobiND(z, k))^(2)- 1)*(1 -1 - (k)^(2)*(JacobiND(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiND[z, (k)^2], z])^(2) == ((JacobiND[z, (k)^2])^(2)- 1)*(1 -1 - (k)^(2)*(JacobiND[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6693722376+2.965675443*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 15.46527968+2.623409101*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.6693722371173725, 2.965675441063337]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[15.465279679493392, 2.6234090772942062]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E7 22.13.E7] || [[Item:Q7058|<math>\left(\deriv{}{z}\Jacobielldck@{z}{k}\right)^{2} = \left(\Jacobielldck^{2}@{z}{k}-1\right)\left(\Jacobielldck^{2}@{z}{k}-k^{2}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiDC(z, k), z))^(2) = ((JacobiDC(z, k))^(2)- 1)*((JacobiDC(z, k))^(2)- (k)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiDC[z, (k)^2], z])^(2) == ((JacobiDC[z, (k)^2])^(2)- 1)*((JacobiDC[z, (k)^2])^(2)- (k)^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E8 22.13.E8] || [[Item:Q7059|<math>\left(\deriv{}{z}\Jacobiellnck@{z}{k}\right)^{2} = {\left(k^{2}+{k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}\right)}{\left(\Jacobiellnck^{2}@{z}{k}-1\right)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiNC(z, k), z))^(2) = ((k)^(2)+1 - (k)^(2)*(JacobiNC(z, k))^(2))*((JacobiNC(z, k))^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiNC[z, (k)^2], z])^(2) == ((k)^(2)+1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2))*((JacobiNC[z, (k)^2])^(2)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.244125150+.6620171546*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .726292651-.1255426739*I
Test Values: {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 [20 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2441251486756877, 0.66201715389323]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.726292650669289, -0.12554267275387493]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E9 22.13.E9] || [[Item:Q7060|<math>\left(\deriv{}{z}\Jacobiellsck@{z}{k}\right)^{2} = \left(1+\Jacobiellsck^{2}@{z}{k}\right)\left(1+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiSC(z, k), z))^(2) = (1 + (JacobiSC(z, k))^(2))*(1 +1 - (k)^(2)*(JacobiSC(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiSC[z, (k)^2], z])^(2) == (1 + (JacobiSC[z, (k)^2])^(2))*(1 +1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.244125150+.6620171546*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.273707349-.1255426740*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.244125148675687, 0.6620171538932291]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.27370734933071006, -0.12554267275387854]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E10 22.13.E10] || [[Item:Q7061|<math>\left(\deriv{}{z}\Jacobiellnsk@{z}{k}\right)^{2} = \left(\Jacobiellnsk^{2}@{z}{k}-k^{2}\right)\left(\Jacobiellnsk^{2}@{z}{k}-1\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiNS(z, k), z))^(2) = ((JacobiNS(z, k))^(2)- (k)^(2))*((JacobiNS(z, k))^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiNS[z, (k)^2], z])^(2) == ((JacobiNS[z, (k)^2])^(2)- (k)^(2))*((JacobiNS[z, (k)^2])^(2)- 1)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E11 22.13.E11] || [[Item:Q7062|<math>\left(\deriv{}{z}\Jacobielldsk@{z}{k}\right)^{2} = \left(\Jacobielldsk^{2}@{z}{k}-{k^{\prime}}^{2}\right)\left(k^{2}+\Jacobielldsk^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiDS(z, k), z))^(2) = ((JacobiDS(z, k))^(2)-1 - (k)^(2))*((k)^(2)+ (JacobiDS(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiDS[z, (k)^2], z])^(2) == ((JacobiDS[z, (k)^2])^(2)-1 - (k)^(2))*((k)^(2)+ (JacobiDS[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.407829919-1.634616811*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 17.28421715+.7965017848*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.4078299188565357, -1.6346168126100018]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[17.284217154319762, 0.7965017768592271]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E12 22.13.E12] || [[Item:Q7063|<math>\left(\deriv{}{z}\Jacobiellcsk@{z}{k}\right)^{2} = \left(1+\Jacobiellcsk^{2}@{z}{k}\right)\left({k^{\prime}}^{2}+\Jacobiellcsk^{2}@{z}{k}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(diff(JacobiCS(z, k), z))^(2) = (1 + (JacobiCS(z, k))^(2))*(1 - (k)^(2)+ (JacobiCS(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[JacobiCS[z, (k)^2], z])^(2) == (1 + (JacobiCS[z, (k)^2])^(2))*(1 - (k)^(2)+ (JacobiCS[z, (k)^2])^(2))</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E13 22.13.E13] || [[Item:Q7064|<math>\deriv[2]{}{z}\Jacobiellsnk@{z}{k} = -(1+k^{2})\Jacobiellsnk@{z}{k}+2k^{2}\Jacobiellsnk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiSN(z, k), [z$(2)]) = -(1 + (k)^(2))*JacobiSN(z, k)+ 2*(k)^(2)* (JacobiSN(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiSN[z, (k)^2], {z, 2}] == -(1 + (k)^(2))*JacobiSN[z, (k)^2]+ 2*(k)^(2)* (JacobiSN[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E14 22.13.E14] || [[Item:Q7065|<math>\deriv[2]{}{z}\Jacobiellcnk@{z}{k} = -({k^{\prime}}^{2}-k^{2})\Jacobiellcnk@{z}{k}-2k^{2}\Jacobiellcnk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiCN(z, k), [z$(2)]) = -(1 - (k)^(2)- (k)^(2))*JacobiCN(z, k)- 2*(k)^(2)* (JacobiCN(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiCN[z, (k)^2], {z, 2}] == -(1 - (k)^(2)- (k)^(2))*JacobiCN[z, (k)^2]- 2*(k)^(2)* (JacobiCN[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E15 22.13.E15] || [[Item:Q7066|<math>\deriv[2]{}{z}\Jacobielldnk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobielldnk@{z}{k}-2\Jacobielldnk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiDN(z, k), [z$(2)]) = (1 +1 - (k)^(2))*JacobiDN(z, k)- 2*(JacobiDN(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiDN[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))*JacobiDN[z, (k)^2]- 2*(JacobiDN[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E16 22.13.E16] || [[Item:Q7067|<math>\deriv[2]{}{z}\Jacobiellcdk@{z}{k} = -(1+k^{2})\Jacobiellcdk@{z}{k}+2k^{2}\Jacobiellcdk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiCD(z, k), [z$(2)]) = -(1 + (k)^(2))*JacobiCD(z, k)+ 2*(k)^(2)* (JacobiCD(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiCD[z, (k)^2], {z, 2}] == -(1 + (k)^(2))*JacobiCD[z, (k)^2]+ 2*(k)^(2)* (JacobiCD[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E17 22.13.E17] || [[Item:Q7068|<math>\deriv[2]{}{z}\Jacobiellsdk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellsdk@{z}{k}-2k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiSD(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))*JacobiSD(z, k)- 2*(k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiSD[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))*JacobiSD[z, (k)^2]- 2*(k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.191457484+2.523217914*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 8.747979617-5.269762671*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.1914574835245033, 2.523217912470552]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[8.747979609525483, -5.269762670615425]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E18 22.13.E18] || [[Item:Q7069|<math>\deriv[2]{}{z}\Jacobiellndk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellndk@{z}{k}-2{k^{\prime}}^{2}\Jacobiellndk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiND(z, k), [z$(2)]) = (1 +1 - (k)^(2))*JacobiND(z, k)- 2*1 - (k)^(2)*(JacobiND(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiND[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))*JacobiND[z, (k)^2]- 2*1 - (k)^(2)*(JacobiND[z, (k)^2])^(3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.040301731+2.018052700*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.903394000-12.57828103*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.0403017307041966, 2.01805269920667]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.903393981406644, -12.578281030301023]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E19 22.13.E19] || [[Item:Q7070|<math>\deriv[2]{}{z}\Jacobielldck@{z}{k} = -(1+k^{2})\Jacobielldck@{z}{k}+2\Jacobielldck^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiDC(z, k), [z$(2)]) = -(1 + (k)^(2))*JacobiDC(z, k)+ 2*(JacobiDC(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiDC[z, (k)^2], {z, 2}] == -(1 + (k)^(2))*JacobiDC[z, (k)^2]+ 2*(JacobiDC[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E20 22.13.E20] || [[Item:Q7071|<math>\deriv[2]{}{z}\Jacobiellnck@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellnck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellnck^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiNC(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))*JacobiNC(z, k)+ 2*1 - (k)^(2)*(JacobiNC(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiNC[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))*JacobiNC[z, (k)^2]+ 2*1 - (k)^(2)*(JacobiNC[z, (k)^2])^(3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.495832765+2.956203453*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.847566639+.844372345e-1*I
Test Values: {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 [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.4958327644324174, 2.9562034517436775]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.8475666387741003, 0.08443723368166078]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E21 22.13.E21] || [[Item:Q7072|<math>\deriv[2]{}{z}\Jacobiellsck@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellsck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellsck^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiSC(z, k), [z$(2)]) = (1 +1 - (k)^(2))*JacobiSC(z, k)+ 2*1 - (k)^(2)*(JacobiSC(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiSC[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))*JacobiSC[z, (k)^2]+ 2*1 - (k)^(2)*(JacobiSC[z, (k)^2])^(3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.525815950+1.181755196*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.577866152+.2036740201*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.5258159501097865, 1.1817551948561285]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.5778661524913966, 0.20367401847233424]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E22 22.13.E22] || [[Item:Q7073|<math>\deriv[2]{}{z}\Jacobiellnsk@{z}{k} = -(1+k^{2})\Jacobiellnsk@{z}{k}+2\Jacobiellnsk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiNS(z, k), [z$(2)]) = -(1 + (k)^(2))*JacobiNS(z, k)+ 2*(JacobiNS(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiNS[z, (k)^2], {z, 2}] == -(1 + (k)^(2))*JacobiNS[z, (k)^2]+ 2*(JacobiNS[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.13.E23 22.13.E23] || [[Item:Q7074|<math>\deriv[2]{}{z}\Jacobielldsk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobielldsk@{z}{k}+2\Jacobielldsk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiDS(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))*JacobiDS(z, k)+ 2*(JacobiDS(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiDS[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))*JacobiDS[z, (k)^2]+ 2*(JacobiDS[z, (k)^2])^(3)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.446566498-1.129997698*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2935291263-10.85414309*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.4465664983977982, -1.1299976975966786]
Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.293529123621927, -10.854143085101464]
Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.13.E24 22.13.E24] || [[Item:Q7075|<math>\deriv[2]{}{z}\Jacobiellcsk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellcsk@{z}{k}+2\Jacobiellcsk^{3}@{z}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(JacobiCS(z, k), [z$(2)]) = (1 +1 - (k)^(2))*JacobiCS(z, k)+ 2*(JacobiCS(z, k))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[JacobiCS[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))*JacobiCS[z, (k)^2]+ 2*(JacobiCS[z, (k)^2])^(3)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.14.E1 22.14.E1] || [[Item:Q7076|<math>\int\Jacobiellsnk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobielldnk@{x}{k}-k\Jacobiellcnk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiSN(x, k), x) = (k)^(- 1)* ln(JacobiDN(x, k)- k*JacobiCN(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiSN[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* Log[JacobiDN[x, (k)^2]- k*JacobiCN[x, (k)^2]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E2 22.14.E2] || [[Item:Q7077|<math>\int\Jacobiellcnk@{x}{k}\diff{x} = k^{-1}\Acos@{\Jacobielldnk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiCN[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* ArcCos[JacobiDN[x, (k)^2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.2690416691147375
Test Values: {Rule[k, 3], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.5226182800392123
Test Values: {Rule[k, 2], Rule[x, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E3 22.14.E3] || [[Item:Q7078|<math>\int\Jacobielldnk@{x}{k}\diff{x} = \Asin@{\Jacobiellsnk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiDN[x, (k)^2], x, GenerateConditions->None] == ArcSin[JacobiSN[x, (k)^2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 6.283185307179586
Test Values: {Rule[k, 3], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 6.283185307179586
Test Values: {Rule[k, 2], Rule[x, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E3 22.14.E3] || [[Item:Q7078|<math>\Asin@{\Jacobiellsnk@{x}{k}} = \Jacobiamk@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcSin[JacobiSN[x, (k)^2]] == JacobiAmplitude[x, Power[k, 2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -6.283185307179586
Test Values: {Rule[k, 3], Rule[x, Rational[3, 2]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/22.14.E4 22.14.E4] || [[Item:Q7079|<math>\int\Jacobiellcdk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobiellndk@{x}{k}+k\Jacobiellsdk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiCD(x, k), x) = (k)^(- 1)* ln(JacobiND(x, k)+ k*JacobiSD(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiCD[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* Log[JacobiND[x, (k)^2]+ k*JacobiSD[x, (k)^2]]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E5 22.14.E5] || [[Item:Q7080|<math>\int\Jacobiellsdk@{x}{k}\diff{x} = (kk^{\prime})^{-1}\Asin@{-k\Jacobiellcdk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiSD[x, (k)^2], x, GenerateConditions->None] == (k*Sqrt[1 - (k)^(2)])^(- 1)* ArcSin[- k*JacobiCD[x, (k)^2]]</syntaxhighlight> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.7955664885698261, 0.9068996821171089]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E6 22.14.E6] || [[Item:Q7081|<math>\int\Jacobiellndk@{x}{k}\diff{x} = {k^{\prime}}^{-1}\Acos@{\Jacobiellcdk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiND[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* ArcCos[JacobiCD[x, (k)^2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[k, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, -1.7320508075688772], Times[-0.3333333333333333, ArcCos[JacobiCD[x, 4.0]], Power[Plus[1.0, Times[-1.0, Power[JacobiCD[x, 4.0], 2]]], Rational[1, 2]], JacobiDN[x, 4.0], Power[JacobiSN[x, 4.0], -1]]]
Test Values: {Rule[k, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E7 22.14.E7] || [[Item:Q7082|<math>\int\Jacobielldck@{x}{k}\diff{x} = \ln@{\Jacobiellnck@{x}{k}+\Jacobiellsck@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiDC(x, k), x) = ln(JacobiNC(x, k)+ JacobiSC(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiDC[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNC[x, (k)^2]+ JacobiSC[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E8 22.14.E8] || [[Item:Q7083|<math>\int\Jacobiellnck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellsck@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiNC(x, k), x) = (sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiSC(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiNC[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiSC[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E9 22.14.E9] || [[Item:Q7084|<math>\int\Jacobiellsck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellnck@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiSC(x, k), x) = (sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiNC(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiSC[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiNC[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E10 22.14.E10] || [[Item:Q7085|<math>\int\Jacobiellnsk@{x}{k}\diff{x} = \ln@{\Jacobielldsk@{x}{k}-\Jacobiellcsk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiNS(x, k), x) = ln(JacobiDS(x, k)- JacobiCS(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiNS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiDS[x, (k)^2]- JacobiCS[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E11 22.14.E11] || [[Item:Q7086|<math>\int\Jacobielldsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobiellcsk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiDS(x, k), x) = ln(JacobiNS(x, k)- JacobiCS(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiDS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNS[x, (k)^2]- JacobiCS[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E12 22.14.E12] || [[Item:Q7087|<math>\int\Jacobiellcsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobielldsk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(JacobiCS(x, k), x) = ln(JacobiNS(x, k)- JacobiDS(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[JacobiCS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNS[x, (k)^2]- JacobiDS[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E13 22.14.E13] || [[Item:Q7088|<math>\int\frac{\diff{x}}{\Jacobiellsnk@{x}{k}} = \ln@{\frac{\Jacobiellsnk@{x}{k}}{\Jacobiellcnk@{x}{k}+\Jacobielldnk@{x}{k}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int((1)/(JacobiSN(x, k)), x) = ln((JacobiSN(x, k))/(JacobiCN(x, k)+ JacobiDN(x, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[1,JacobiSN[x, (k)^2]], x, GenerateConditions->None] == Log[Divide[JacobiSN[x, (k)^2],JacobiCN[x, (k)^2]+ JacobiDN[x, (k)^2]]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E14 22.14.E14] || [[Item:Q7089|<math>\int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk@{x}{k}} = \frac{1}{2}\ln@{\frac{1-\Jacobielldnk@{x}{k}}{1+\Jacobielldnk@{x}{k}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int((JacobiCN(x, k))/(JacobiSN(x, k)), x) = (1)/(2)*ln((1 - JacobiDN(x, k))/(1 + JacobiDN(x, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[JacobiCN[x, (k)^2],JacobiSN[x, (k)^2]], x, GenerateConditions->None] == Divide[1,2]*Log[Divide[1 - JacobiDN[x, (k)^2],1 + JacobiDN[x, (k)^2]]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0.6931471805599452
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.0986122886681102, 3.141592653589793]
Test Values: {Rule[k, 3], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.14.E15 22.14.E15] || [[Item:Q7090|<math>\int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk^{2}@{x}{k}} = -\frac{\Jacobielldnk@{x}{k}}{\Jacobiellsnk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int((JacobiCN(x, k))/((JacobiSN(x, k))^(2)), x) = -(JacobiDN(x, k))/(JacobiSN(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Divide[JacobiCN[x, (k)^2],(JacobiSN[x, (k)^2])^(2)], x, GenerateConditions->None] == -Divide[JacobiDN[x, (k)^2],JacobiSN[x, (k)^2]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.14.E16 22.14.E16] || [[Item:Q7091|<math>\int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellsnk@{t}{k}}\diff{t} = -\tfrac{\cpi}{4}\ccompellintKk@{k}-\tfrac{1}{2}\compellintKk@{k}\ln@@{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(ln(JacobiSN(t, k)), t = 0..EllipticK(k)) = -(Pi)/(4)*EllipticCK(k)-(1)/(2)*EllipticK(k)*ln(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Log[JacobiSN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == -Divide[Pi,4]*EllipticK[1-(k)^2]-Divide[1,2]*EllipticK[(k)^2]*Log[k]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.14.E17 22.14.E17] || [[Item:Q7092|<math>\int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellcnk@{t}{k}}\diff{t} = -\tfrac{\cpi}{4}\ccompellintKk@{k}+\tfrac{1}{2}\compellintKk@{k}\ln@{k^{\prime}/k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(ln(JacobiCN(t, k)), t = 0..EllipticK(k)) = -(Pi)/(4)*EllipticCK(k)+(1)/(2)*EllipticK(k)*ln(sqrt(1 - (k)^(2))/k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Log[JacobiCN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == -Divide[Pi,4]*EllipticK[1-(k)^2]+Divide[1,2]*EllipticK[(k)^2]*Log[Sqrt[1 - (k)^(2)]/k]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.14.E18 22.14.E18] || [[Item:Q7093|<math>\int_{0}^{\compellintKk@{k}}\ln@{\Jacobielldnk@{t}{k}}\diff{t} = \tfrac{1}{2}\compellintKk@{k}\ln@@{k^{\prime}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>int(ln(JacobiDN(t, k)), t = 0..EllipticK(k)) = (1)/(2)*EllipticK(k)*ln(sqrt(1 - (k)^(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Log[JacobiDN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == Divide[1,2]*EllipticK[(k)^2]*Log[Sqrt[1 - (k)^(2)]]</syntaxhighlight> || Failure || Failure || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E1 22.15.E1] || [[Item:Q7094|<math>\Jacobiellsnk@{\xi}{k} = x</math>]] || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>JacobiSN(xi, k) = x</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[\[Xi], (k)^2] == x</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2924027565+.2435601371*I
Test Values: {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1797898601-.1565493762e-1*I
Test Values: {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.29240275641803626, 0.2435601371571337]
Test Values: {Rule[k, 1], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.17978986006074704, -0.015654937469336286]
Test Values: {Rule[k, 2], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E2 22.15.E2] || [[Item:Q7095|<math>\Jacobiellcnk@{\eta}{k} = x</math>]] || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>JacobiCN(eta, k) = x</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[\[Eta], (k)^2] == x</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2107428373-.2715436778*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2337173832+.1450431473e-1*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.21074283744314704, -0.27154367778248023]
Test Values: {Rule[k, 1], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.23371738317128377, 0.01450431459800293]
Test Values: {Rule[k, 2], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E3 22.15.E3] || [[Item:Q7096|<math>\Jacobielldnk@{\zeta}{k} = x</math>]] || <math>k^{\prime} \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>JacobiDN(InverseJacobiDN(x, k), k) = x</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[InverseJacobiDN[x, (k)^2], (k)^2] == x</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/22.15.E5 22.15.E5] || [[Item:Q7100|<math>-K \leq \aJacobiellsnk@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>- EllipticK(k) <= InverseJacobiSN(x, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- EllipticK[(k)^2] <= InverseJacobiSN[x, (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[DirectedInfinity[], Complex[0.8047189562170503, -1.5707963267948966]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-0.8428751774062981, 1.0782578237498217], Complex[0.372543189356477, -1.0782578237498215]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E5 22.15.E5] || [[Item:Q7100|<math>\aJacobiellsnk@{x}{k} \leq K</math>]] || <math></math> || <syntaxhighlight lang=mathematica>InverseJacobiSN(x, k) <= EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiSN[x, (k)^2] <= EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.8047189562170503, -1.5707963267948966], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.372543189356477, -1.0782578237498215], Complex[0.8428751774062981, -1.0782578237498217]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E6 22.15.E6] || [[Item:Q7101|<math>0 \leq \aJacobiellcnk@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>0 <= InverseJacobiCN(x, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 <= InverseJacobiCN[x, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[0.0, 0.8410686705679303]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[5.551115123125783*^-16, 0.6872864564092609]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E6 22.15.E6] || [[Item:Q7101|<math>\aJacobiellcnk@{x}{k} \leq 2K</math>]] || <math></math> || <syntaxhighlight lang=mathematica>InverseJacobiCN(x, k) <= 2*EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiCN[x, (k)^2] <= 2*EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[5.551115123125783*^-16, 0.6872864564092609], Complex[1.6857503548125963, -2.1565156474996434]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E7 22.15.E7] || [[Item:Q7102|<math>0 \leq \aJacobielldnk@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>0 <= InverseJacobiDN(x, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>0 <= InverseJacobiDN[x, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[0.0, 0.8410686705679303]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.0, Complex[1.6857503548125963, -1.6950867772240739]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E7 22.15.E7] || [[Item:Q7102|<math>\aJacobielldnk@{x}{k} \leq K</math>]] || <math></math> || <syntaxhighlight lang=mathematica>InverseJacobiDN(x, k) <= EllipticK(k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiDN[x, (k)^2] <= EllipticK[(k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[1.6857503548125963, -1.6950867772240739], Complex[0.8428751774062981, -1.0782578237498217]]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E8 22.15.E8] || [[Item:Q7103|<math>\xi = (-1)^{m}\aJacobiellsnk@{x}{k}+2mK</math>]] || <math></math> || <syntaxhighlight lang=mathematica>xi = (- 1)^(m)* InverseJacobiSN(x, k)+ 2*m*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Xi] == (- 1)^(m)* InverseJacobiSN[x, (k)^2]+ 2*m*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.613064478e-1-2.070796327*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.402795168+.70796327e-1*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.061306447567388456, -2.0707963267948966]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.4027951675703663, 0.07079632679489672]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E9 22.15.E9] || [[Item:Q7104|<math>\eta = +\aJacobiellcnk@{x}{k}+4mK</math>]] || <math></math> || <syntaxhighlight lang=mathematica>eta = + InverseJacobiCN(x, k)+ 4*m*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta] == + InverseJacobiCN[x, (k)^2]+ 4*m*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.598076212-2.341068671*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.062177828-4.341068671*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.598076211353316, -2.34106867056793]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-6.062177826491071, -4.34106867056793]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E9 22.15.E9] || [[Item:Q7104|<math>\eta = -\aJacobiellcnk@{x}{k}+4mK</math>]] || <math></math> || <syntaxhighlight lang=mathematica>eta = - InverseJacobiCN(x, k)+ 4*m*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta] == - InverseJacobiCN[x, (k)^2]+ 4*m*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.598076212-.6589313294*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.062177828-2.658931329*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.598076211353316, -0.6589313294320696]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-6.062177826491071, -2.658931329432069]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E10 22.15.E10] || [[Item:Q7105|<math>\zeta = +\aJacobielldnk@{x}{k}+2mK</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(InverseJacobiDN(x, k)) = + InverseJacobiDN(x, k)+ 2*m*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>(InverseJacobiDN[x, (k)^2]) == + InverseJacobiDN[x, (k)^2]+ 2*m*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.732050808-1.000000000*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.464101616-2.*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.7320508075688774, -0.9999999999999999]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.464101615137755, -1.9999999999999998]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E10 22.15.E10] || [[Item:Q7105|<math>\zeta = -\aJacobielldnk@{x}{k}+2mK</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(InverseJacobiDN(x, k)) = - InverseJacobiDN(x, k)+ 2*m*K</syntaxhighlight> || <syntaxhighlight lang=mathematica>(InverseJacobiDN[x, (k)^2]) == - InverseJacobiDN[x, (k)^2]+ 2*m*K</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.732050808+.682137341*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.464101616-.317862659*I
Test Values: {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [270 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.7320508075688774, 0.6821373411358608]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.464101615137755, -0.3178626588641391]
Test Values: {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.15.E11 22.15.E11] || [[Item:Q7106|<math>x = \int_{0}^{\Jacobiellsnk@{x}{k}}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}</math>]] || <math>-1 \leq x, x \leq 1, 0 \leq k, k \leq 1</math> || <syntaxhighlight lang=mathematica>x = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..JacobiSN(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, JacobiSN[x, (k)^2]}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 1] || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E12 22.15.E12] || [[Item:Q7107|<math>\aJacobiellsnk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}</math>]] || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>InverseJacobiSN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiSN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E13 22.15.E13] || [[Item:Q7108|<math>\aJacobiellcnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}}</math>]] || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>InverseJacobiCN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2)))), t = x..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiCN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E14 22.15.E14] || [[Item:Q7109|<math>\aJacobielldnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}}</math>]] || <math>k^{\prime} \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>InverseJacobiDN(x, k) = int((1)/(sqrt((1 - (t)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiDN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, 1}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E15 22.15.E15] || [[Item:Q7110|<math>\aJacobiellcdk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}</math>]] || <math>-1 \leq x, x \leq 1</math> || <syntaxhighlight lang=mathematica>InverseJacobiCD(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = x..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiCD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E16 22.15.E16] || [[Item:Q7111|<math>\aJacobiellsdk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}}</math>]] || <math>-1/k^{\prime} \leq x, x \leq 1/k^{\prime}</math> || <syntaxhighlight lang=mathematica>InverseJacobiSD(x, k) = int((1)/(sqrt((1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2)))), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiSD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Skip - No test values generated
|-
| [https://dlmf.nist.gov/22.15.E17 22.15.E17] || [[Item:Q7112|<math>\aJacobiellndk@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(1-{k^{\prime}}^{2}t^{2})}}</math>]] || <math>1 \leq x, x \leq 1/k^{\prime}</math> || <syntaxhighlight lang=mathematica>InverseJacobiND(x, k) = int((1)/(sqrt(((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2)))), t = 1..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiND[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Skip - No test values generated
|-
| [https://dlmf.nist.gov/22.15.E18 22.15.E18] || [[Item:Q7113|<math>\aJacobielldck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}</math>]] || <math>1 \leq x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiDC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = 1..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiDC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, 1, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E19 22.15.E19] || [[Item:Q7114|<math>\aJacobiellnck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}}</math>]] || <math>1 \leq x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiNC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2)))), t = 1..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiNC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E20 22.15.E20] || [[Item:Q7115|<math>\aJacobiellsck@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}}</math>]] || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiSC(x, k) = int((1)/(sqrt((1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2)))), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiSC[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2))]], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E21 22.15.E21] || [[Item:Q7116|<math>\aJacobiellnsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}</math>]] || <math>1 \leq x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiNS(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = x..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiNS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E22 22.15.E22] || [[Item:Q7117|<math>\aJacobielldsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}}</math>]] || <math>k^{\prime} \leq x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiDS(x, k) = int((1)/(sqrt(((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiDS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.15.E23 22.15.E23] || [[Item:Q7118|<math>\aJacobiellcsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}}</math>]] || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>InverseJacobiCS(x, k) = int((1)/(sqrt((1 + (t)^(2))*((t)^(2)+1 - (k)^(2)))), t = x..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>InverseJacobiCS[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*((t)^(2)+1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/22.16.E1 22.16.E1] || [[Item:Q7120|<math>\Jacobiamk@{x}{k} = \Asin@{\Jacobiellsnk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[k, 2]] == ArcSin[JacobiSN[x, (k)^2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 6.283185307179586
Test Values: {Rule[k, 3], Rule[x, Rational[3, 2]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/22.16.E2 22.16.E2] || [[Item:Q7121|<math>\Jacobiamk@{x+2K}{k} = \Jacobiamk@{x}{k}+\pi</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiAM(x + 2*EllipticK(k), k) = JacobiAM(x, k)+ Pi</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x + 2*EllipticK[(k)^2], Power[k, 2]] == JacobiAmplitude[x, Power[k, 2]]+ Pi</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-4.273320998840302, Gudermannian[DirectedInfinity[]]]
Test Values: {Rule[k, 1], Rule[x, Rational[3, 2]]}</syntaxhighlight><br></div></div>
|-
| [https://dlmf.nist.gov/22.16.E3 22.16.E3] || [[Item:Q7122|<math>\Jacobiamk@{x}{k} = \int_{0}^{x}\Jacobielldnk@{t}{k}\diff{t}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiAM(x, k) = int(JacobiDN(t, k), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[k, 2]] == Integrate[JacobiDN[t, (k)^2], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 9] || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/22.16.E4 22.16.E4] || [[Item:Q7123|<math>\Jacobiamk@{x}{0} = x</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiAM(x, 0) = x</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[0, 2]] == x</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/22.16.E5 22.16.E5] || [[Item:Q7124|<math>\Jacobiamk@{x}{1} = \Gudermannian@{x}</math>]] || <math>-\infty < x, x < \infty</math> || <syntaxhighlight lang=mathematica>JacobiAM(x, 1) = arctan(sinh(x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[1, 2]] == Gudermannian[x]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/22.16.E9 22.16.E9] || [[Item:Q7128|<math>\Jacobiamk@{x}{k} = \frac{\pi}{2K}x+2\sum_{n=1}^{\infty}\frac{q^{n}\sin@{2n\zeta}}{n(1+q^{2n})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiAM(x, k) = (Pi)/(2*EllipticK(k))*x + 2*sum(((exp(- Pi*EllipticCK(k)/EllipticK(k)))^(n)* sin(2*n*zeta))/(n*(1 +(exp(- Pi*EllipticCK(k)/EllipticK(k)))^(2*n))), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[k, 2]] == Divide[Pi,2*EllipticK[(k)^2]]*x + 2*Sum[Divide[(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(n)* Sin[2*n*\[Zeta]],n*(1 +(Exp[- Pi*EllipticK[1-(k)^2]/EllipticK[(k)^2]])^(2*n))], {n, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[1.9977537490349477, 0.49999999999999994], Times[-1.0, Gudermannian[DirectedInfinity[]]]]
Test Values: {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.6288351638274511, -0.8359897636003678]
Test Values: {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E10 22.16.E10] || [[Item:Q7129|<math>x = \incellintFk@{\phi}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x = EllipticF(sin(phi), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == EllipticF[\[Phi], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6791299710-.6773780507*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.016811658-.7182528229*I
Test Values: {phi = 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 [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6791299712710547, -0.6773780505641274]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.0168116579433883, -0.7182528227883367]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E11 22.16.E11] || [[Item:Q7130|<math>\Jacobiamk@{x}{k} = \phi</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiAM(x, k) = phi</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiAmplitude[x, Power[k, 2]] == \[Phi]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2657029410-.5000000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6844899651-.5000000000*I
Test Values: {phi = 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 [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.26570294146607043, -0.49999999999999994]
Test Values: {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.6844899649247672, -0.49999999999999994]
Test Values: {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E12 22.16.E12] || [[Item:Q7131|<math>\Jacobiellsnk@{x}{k} = \sin@@{\phi}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(x, k) = sin(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[x, (k)^2] == Sin[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .461679191e-1-.3375964631*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6784403409-.3375964631*I
Test Values: {phi = 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 [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.046167919344728525, -0.33759646322287]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.678440340667692, -0.33759646322287]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E12 22.16.E12] || [[Item:Q7131|<math>\sin@@{\phi} = \sin@{\Jacobiamk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sin(phi) = sin(JacobiAM(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[\[Phi]] == Sin[JacobiAmplitude[x, Power[k, 2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.461679191e-1+.3375964631*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6784403409+.3375964631*I
Test Values: {phi = 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 [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.046167919344728525, 0.33759646322287]
Test Values: {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.678440340667692, 0.33759646322287]
Test Values: {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E13 22.16.E13] || [[Item:Q7132|<math>\Jacobiellcnk@{x}{k} = \cos@@{\phi}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(x, k) = cos(phi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[x, (k)^2] == Cos[\[Phi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3054469840+.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2530246253+.3969495503*I
Test Values: {phi = 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 [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.3054469841149447, 0.3969495502290325]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.2530246251336542, 0.3969495502290325]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E13 22.16.E13] || [[Item:Q7132|<math>\cos@@{\phi} = \cos@{\Jacobiamk@{x}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>cos(phi) = cos(JacobiAM(x, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[\[Phi]] == Cos[JacobiAmplitude[x, Power[k, 2]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3054469840-.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2530246253-.3969495503*I
Test Values: {phi = 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 [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.3054469841149447, -0.3969495502290325]
Test Values: {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.2530246251336542, -0.3969495502290325]
Test Values: {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E33 22.16.E33] || [[Item:Q7153|<math>\JacobiZetak@{x+K}{k} = \JacobiZetak@{x}{k}-k^{2}\Jacobiellsnk@{x}{k}\Jacobiellcdk@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiZeta(x + EllipticK(k), k) = JacobiZeta(x, k)- (k)^(2)* JacobiSN(x, k)*JacobiCD(x, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiZeta[x + EllipticK[(k)^2], k] == JacobiZeta[x, k]- (k)^(2)* JacobiSN[x, (k)^2]*JacobiCD[x, (k)^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.09234673295918805, JacobiZeta[DirectedInfinity[], 1.0]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.7319699839312124, -0.6260098794347219]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.16.E34 22.16.E34] || [[Item:Q7154|<math>\JacobiZetak@{x+2K}{k} = \JacobiZetak@{x}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiZeta(x + 2*EllipticK(k), k) = JacobiZeta(x, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiZeta[x + 2*EllipticK[(k)^2], k] == JacobiZeta[x, k]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-0.9974949866040544, JacobiZeta[DirectedInfinity[], 1.0]]
Test Values: {Rule[k, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.2870190432201134, -5.437509139287473]
Test Values: {Rule[k, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.17.E1 22.17.E1] || [[Item:Q7155|<math>\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.17.E2 22.17.E2] || [[Item:Q7156|<math>\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.17.E3 22.17.E3] || [[Item:Q7157|<math>\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(z, 1/k) = JacobiDN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.17.E4 22.17.E4] || [[Item:Q7158|<math>\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(z, 1/k) = JacobiCN(z/k, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/22.18.E1 22.18.E1] || [[Item:Q7164|<math>\left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right) = 1</math>]] || <math></math> || <syntaxhighlight lang=mathematica>((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>((x)^(2)/(a)^(2))+((y)^(2)/(b)^(2)) == 1</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.18#Ex1 22.18#Ex1] || [[Item:Q7165|<math>x = a\Jacobiellsnk@{u}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x = a*JacobiSN(u, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == a*JacobiSN[u, (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.688604135+.3653402056*I
Test Values: {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.519684790-.2348240643e-1*I
Test Values: {a = -3/2, u = 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[2.688604134627054, 0.3653402057357006]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.5196847900911203, -0.02348240620400443]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.18#Ex2 22.18#Ex2] || [[Item:Q7166|<math>y = b\Jacobiellcnk@{u}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>y = b*JacobiCN(u, k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>y == b*JacobiCN[u, (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.433885744-.4073155167*I
Test Values: {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.399423925+.2175647210e-1*I
Test Values: {b = -3/2, u = 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: Complex[-0.43388574383527945, -0.40731551667372035]
Test Values: {Rule[b, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.39942392524307424, 0.021756471897004394]
Test Values: {Rule[b, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.18.E4 22.18.E4] || [[Item:Q7168|<math>l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>l(r) = (1/(sqrt(2)))*InverseJacobiCN(r, 1/(sqrt(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>l[r] == (1/(Sqrt[2]))*InverseJacobiCN[r, (1/(Sqrt[2]))^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.122057553+.6299669258*I
Test Values: {r = -3/2, l = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -5.622057553+.6299669258*I
Test Values: {r = -3/2, l = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-4.12205755429212, 0.629966925905157]
Test Values: {Rule[l, 1], Rule[r, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-5.62205755429212, 0.629966925905157]
Test Values: {Rule[l, 2], Rule[r, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.18.E5 22.18.E5] || [[Item:Q7169|<math>r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>r = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>r == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.810737930
Test Values: {r = -3/2, l = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8262668012
Test Values: {r = -3/2, l = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.810737930333856
Test Values: {Rule[l, 1], Rule[r, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -0.8262668010254658
Test Values: {Rule[l, 2], Rule[r, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.18#Ex3 22.18#Ex3] || [[Item:Q7170|<math>x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))*JacobiDN(sqrt(2)*l, 1/(sqrt(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>x == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]*JacobiDN[Sqrt[2]*l, (1/(Sqrt[2]))^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.269911408
Test Values: {x = 3/2, l = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.074437352
Test Values: {x = 3/2, l = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.2699114077583538
Test Values: {Rule[l, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.0744373520381156
Test Values: {Rule[l, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.18.E7 22.18.E7] || [[Item:Q7172|<math>ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f = 0</math>]] || <math></math> || <syntaxhighlight lang=mathematica>a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + exp(1)*(x + y)+ f = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + E*(x + y)+ f == 0</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.18#Ex5 22.18#Ex5] || [[Item:Q7173|<math>x_{3} = \frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x[3] = (x[1]*y[2]+ x[2]*y[1])/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, 3] == Divide[Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1],1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.18#Ex6 22.18#Ex6] || [[Item:Q7174|<math>y_{3} = \frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>y[3] = (y[1]*y[2]+ x[2]*(-(1 + (k)^(2))*x[1]+ 2*(k)^(2)* (x[1])^(3)))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))+ x[3]*(2*(k)^(2)* x[1]*y[1]*(x[2])^(2))/(1 - (k)^(2)* (x[1])^(2)*(x[2])^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[y, 3] == Divide[Subscript[y, 1]*Subscript[y, 2]+ Subscript[x, 2]*(-(1 + (k)^(2))*Subscript[x, 1]+ 2*(k)^(2)* (Subscript[x, 1])^(3)),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]+ Subscript[x, 3]*Divide[2*(k)^(2)* Subscript[x, 1]*Subscript[y, 1]*(Subscript[x, 2])^(2),1 - (k)^(2)* (Subscript[x, 1])^(2)*(Subscript[x, 2])^(2)]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.19.E1 22.19.E1] || [[Item:Q7175|<math>\deriv[2]{\theta(t)}{t} = -\sin@@{\theta(t)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>diff(theta(t), [t$(2)]) = - sin(theta(t))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[\[Theta][t], {t, 2}] == - Sin[\[Theta][t]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.247168970-.2207308174*I
Test Values: {t = -3/2, theta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.342338585-1.241300956*I
Test Values: {t = -3/2, theta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.247168970138959, -0.22073081765616068]
Test Values: {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.3423385844153726, -1.2413009551766627]
Test Values: {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E2 22.19.E2] || [[Item:Q7176|<math>\sin@{\tfrac{1}{2}\theta(t)} = \sin@{\frac{1}{2}\alpha}\Jacobiellsnk@{t+K}{\sin@{\tfrac{1}{2}\alpha}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sin((1)/(2)*theta(t)) = sin((1)/(2)*alpha)*JacobiSN(t + EllipticK(k), sin((1)/(2)*alpha))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[Divide[1,2]*\[Theta][t]] == Sin[Divide[1,2]*\[Alpha]]*JacobiSN[t + EllipticK[(k)^2], (Sin[Divide[1,2]*\[Alpha]])^2]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.6478293894548304, -0.30568930559799934], Times[-0.6816387600233341, JacobiSN[DirectedInfinity[], 0.4646313991661485]]]
Test Values: {Rule[k, 1], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.12355997139036334, 0.2467451262932382]
Test Values: {Rule[k, 2], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E3 22.19.E3] || [[Item:Q7177|<math>\theta(t) = 2\Jacobiamk@{t\sqrt{E/2}}{\sqrt{2/E}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>theta(t) = 2*JacobiAM(t*sqrt(E/2), sqrt(2/E))</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Theta][t] == 2*JacobiAmplitude[t*Sqrt[E/2], Power[Sqrt[2/E], 2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .133442481-.3164102922*I
Test Values: {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.182480587-.8654483982*I
Test Values: {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.13344248094652933, -0.31641029231150586]
Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.182480586623187, -0.865448397988164]
Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E5 22.19.E5] || [[Item:Q7179|<math>V(x) = +\tfrac{1}{2}x^{2}+\tfrac{1}{4}\beta x^{4}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>V(x) = +(1)/(2)*(x)^(2)+(1)/(4)*beta*(x)^(4)</syntaxhighlight> || <syntaxhighlight lang=mathematica>V[x] == +Divide[1,2]*(x)^(2)+Divide[1,4]*\[Beta]*(x)^(4)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.19.E6 22.19.E6] || [[Item:Q7180|<math>x(t) = a\Jacobiellcnk@{t\sqrt{1+2\eta}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x(t) = a*JacobiCN(t*sqrt(1 + 2*eta), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x[t] == a*JacobiCN[t*Sqrt[1 + 2*\[Eta]], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.032489573-.1028075729*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.103953626-.7415756720e-2*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -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[-2.032489572589819, -0.10280757291863922]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.103953626215099, -0.007415756590236153]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E7 22.19.E7] || [[Item:Q7181|<math>x(t) = a\Jacobiellsnk@{t\sqrt{1-\eta}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x(t) = a*JacobiSN(t*sqrt(1 - eta), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x[t] == a*JacobiSN[t*Sqrt[1 - \[Eta]], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.540811611+.4656977091*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.440732980-.1498418752e-1*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -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[-3.5408116110434387, 0.46569770889881135]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.4407329797279083, -0.014984187659583321]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E8 22.19.E8] || [[Item:Q7182|<math>x(t) = a\Jacobielldnk@{t\sqrt{\eta}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x(t) = a*JacobiDN(t*sqrt(eta), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x[t] == a*JacobiDN[t*Sqrt[\[Eta]], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.613955183-.2329422536*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.968457087-.6161541466*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -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[-1.6139551823182394, -0.23294225362869586]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.968457085129692, -0.6161541479869231]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.19.E9 22.19.E9] || [[Item:Q7183|<math>x(t) = a\Jacobiellcnk@{t\sqrt{2\eta-1}}{k}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>x(t) = a*JacobiCN(t*sqrt(2*eta - 1), k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>x[t] == a*JacobiCN[t*Sqrt[2*\[Eta]- 1], (k)^2]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.736815452-.4365167404*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.272323884+.8696505748*I
Test Values: {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -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[-1.7368154521565795, -0.4365167405198458]
Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.27232388329398516, 0.8696505752545954]
Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.20#Ex1 22.20#Ex1] || [[Item:Q7184|<math>a_{n} = \tfrac{1}{2}\left(a_{n-1}+b_{n-1}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>a[n] = (1)/(2)*(a[n - 1]+ b[n - 1])</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, n] == Divide[1,2]*(Subscript[a, n - 1]+ Subscript[b, n - 1])</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.20#Ex2 22.20#Ex2] || [[Item:Q7185|<math>b_{n} = \left(a_{n-1}b_{n-1}\right)^{1/2}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>b[n] = (a[n - 1]*b[n - 1])^(1/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[b, n] == (Subscript[a, n - 1]*Subscript[b, n - 1])^(1/2)</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.20#Ex3 22.20#Ex3] || [[Item:Q7186|<math>c_{n} = \tfrac{1}{2}\left(a_{n-1}-b_{n-1}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>c[n] = (1)/(2)*(a[n - 1]- b[n - 1])</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, n] == Divide[1,2]*(Subscript[a, n - 1]- Subscript[b, n - 1])</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.20.E3 22.20.E3] || [[Item:Q7188|<math>\phi_{N} = 2^{N}a_{N}x</math>]] || <math></math> || <syntaxhighlight lang=mathematica>phi[N] = (2)^(N)* a[N]*x</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Phi], N] == (2)^(N)* Subscript[a, N]*x</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/22.20.E4 22.20.E4] || [[Item:Q7189|<math>\phi_{n-1} = \frac{1}{2}\left(\phi_{n}+\asin@{\frac{c_{n}}{a_{n}}\sin@@{\phi_{n}}}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>phi[n - 1] = (1)/(2)*(phi[n]+ arcsin((c[n])/(a[n])*sin(phi[n])))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Phi], n - 1] == Divide[1,2]*(Subscript[\[Phi], n]+ ArcSin[Divide[Subscript[c, n],Subscript[a, n]]*Sin[Subscript[\[Phi], n]]])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.366025404+.3660254040*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, c[n] = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, phi[-1+n] = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.366025404+.3660254040*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, c[n] = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, phi[-1+n] = -1/2+1/2*I*3^(1/2), n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [276 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3660254037844384, -0.36602540378443876]
Test Values: {Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.3660254037844384, -0.36602540378443876]
Test Values: {Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip e</div></div>
|-
| [https://dlmf.nist.gov/22.20#Ex4 22.20#Ex4] || [[Item:Q7190|<math>\Jacobiellsnk@{x}{k} = \sin@@{\phi_{0}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(x, k) = sin(phi[0])</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[x, (k)^2] == Sin[Subscript[\[Phi], 0]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .461679191e-1-.3375964631*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6784403409-.3375964631*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.046167919344728525, -0.33759646322287]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.678440340667692, -0.33759646322287]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.20#Ex5 22.20#Ex5] || [[Item:Q7191|<math>\Jacobiellcnk@{x}{k} = \cos@@{\phi_{0}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(x, k) = cos(phi[0])</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[x, (k)^2] == Cos[Subscript[\[Phi], 0]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3054469840+.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2530246253+.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.3054469841149447, 0.3969495502290325]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.2530246251336542, 0.3969495502290325]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.20#Ex6 22.20#Ex6] || [[Item:Q7192|<math>\Jacobielldnk@{x}{k} = \frac{\cos@@{\phi_{0}}}{\cos@{\phi_{1}-\phi_{0}}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(x, k) = (cos(phi[0]))/(cos(phi[1]- phi[0]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[x, (k)^2] == Divide[Cos[Subscript[\[Phi], 0]],Cos[Subscript[\[Phi], 1]- Subscript[\[Phi], 0]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3054469840+.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, phi[1] = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.663077867+.3969495503*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, phi[1] = 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[-0.3054469841149447, 0.3969495502290325]
Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.6630778670906836, 0.3969495502290325]
Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-
| [https://dlmf.nist.gov/22.20#Ex7 22.20#Ex7] || [[Item:Q7193|<math>K = \frac{\pi}{2M(1,k^{\prime})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>EllipticK(k) = (Pi)/(2*M(1 ,sqrt(1 - (k)^(2))))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EllipticK[(k)^2] == Divide[Pi,2*M[1 ,Sqrt[1 - (k)^(2)]]]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
|}

Latest revision as of 17:37, 25 May 2021

Notation
22.1 Special Notation
Properties
22.2 Definitions
22.3 Graphics
22.4 Periods, Poles, and Zeros
22.5 Special Values
22.6 Elementary Identities
22.7 Landen Transformations
22.8 Addition Theorems
22.9 Cyclic Identities
22.10 Maclaurin Series
22.11 Fourier and Hyperbolic Series
22.12 Expansions in Other Trigonometric Series and Doubly-Infinite Partial Fractions: Eisenstein Series
22.13 Derivatives and Differential Equations
22.14 Integrals
22.15 Inverse Functions
22.16 Related Functions
22.17 Moduli Outside the Interval [0,1]
Applications
22.18 Mathematical Applications
22.19 Physical Applications
Computation
22.20 Methods of Computation
22.21 Tables
22.22 Software
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