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Results of Lamé Functions - Revision history
2024-03-29T15:33:28Z
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Admin: Created page with "{| class="wikitable sortable" |- ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica |- | [..."
2020-01-19T14:27:18Z
<p>Created page with "{| class="wikitable sortable" |- ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica |- | [..."</p>
<p><b>New page</b></p><div>{| class="wikitable sortable"<br />
|-<br />
! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica<br />
|-<br />
| [https://dlmf.nist.gov/29.2.E1 29.2.E1] || [[Item:Q8574|<math>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k})w = 0</math>]] || <code>diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2))* w = 0</code> || <code>D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2))* w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>7.948739768-7.545139452*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>51.95468921+27.97388965*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>-3.910915794-11.82960931*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>6.183103152-8.579425434*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.2.E2 29.2.E2] || [[Item:Q8575|<math>\deriv[2]{w}{\xi}+\frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)\deriv{w}{\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi-k^{-2})}w = 0</math>]] || <code>diff(w, [xi$(2)])+(1)/(2)*((1)/(xi)+(1)/(xi - 1)+(1)/(xi - (k)^(- 2)))* diff(w, xi)+(h*(k)^(- 2)- nu*(nu + 1)* xi)/(4*xi*(xi - 1)*(xi - (k)^(- 2)))*w = 0</code> || <code>D[w, {\[Xi], 2}]+Divide[1,2]*(Divide[1,\[Xi]]+Divide[1,\[Xi]- 1]+Divide[1,\[Xi]- (k)^(- 2)])* D[w, \[Xi]]+Divide[h*(k)^(- 2)- \[Nu]*(\[Nu]+ 1)* \[Xi],4*\[Xi]*(\[Xi]- 1)*(\[Xi]- (k)^(- 2))]*w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.197364586+.3597957455*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>-1.025513349+.2414101023e-1*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>-.9825277432-.7730059408e-2*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>.1006999677+1.062488515*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
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| [https://dlmf.nist.gov/29.2.E4 29.2.E4] || [[Item:Q8577|<math>(1-k^{2}\cos^{2}@@{\phi})\deriv[2]{w}{\phi}+k^{2}\cos@@{\phi}\sin@@{\phi}\deriv{w}{\phi}+(h-\nu(\nu+1)k^{2}\cos^{2}@@{\phi})w = 0</math>]] || <code>(1 - (k)^(2)* (cos(phi))^(2))* diff(w, [phi$(2)])+ (k)^(2)* cos(phi)*sin(phi)*diff(w, phi)+(h - nu*(nu + 1)*(k)^(2)* (cos(phi))^(2))* w = 0</code> || <code>(1 - (k)^(2)* (Cos[\[Phi]])^(2))* D[w, {\[Phi], 2}]+ (k)^(2)* Cos[\[Phi]]*Sin[\[Phi]]*D[w, \[Phi]]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (Cos[\[Phi]])^(2))* w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-32.55364142+30.82095554*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>-130.2145657+111.2838222*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>-292.9827729+245.3885999*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>30.82095554+32.55364142*I <- {h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.2.E10 29.2.E10] || [[Item:Q8584|<math>{\deriv[2]{w}{\zeta}+\frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_{3}}\right)\deriv{w}{\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(\zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w = 0</math>]] || <code>diff(w, [zeta$(2)])+(1)/(2)*((1)/(zeta - e[1])+(1)/(zeta - e[2])+(1)/(zeta - e[3]))* diff(w, zeta)+(g - nu*(nu + 1)* zeta)/(4*(zeta - e[1])*(zeta - e[2])*(zeta - e[3]))*w = 0</code> || <code>D[w, {\[zeta], 2}]+Divide[1,2]*(Divide[1,\[zeta]- Subscript[e, 1]]+Divide[1,\[zeta]- Subscript[e, 2]]+Divide[1,\[zeta]- Subscript[e, 3]])* D[w, \[zeta]]+Divide[g - \[Nu]*(\[Nu]+ 1)* \[zeta],4*(\[zeta]- Subscript[e, 1])*(\[zeta]- Subscript[e, 2])*(\[zeta]- Subscript[e, 3])]*w = 0</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/29.8.E1 29.8.E1] || [[Item:Q8704|<math>x = k^{2}\Jacobiellsnk@{z}{k}\Jacobiellsnk@{z_{1}}{k}\Jacobiellsnk@{z_{2}}{k}\Jacobiellsnk@{z_{3}}{k}-\frac{k^{2}}{{k^{\prime}}^{2}}\Jacobiellcnk@{z}{k}\Jacobiellcnk@{z_{1}}{k}\Jacobiellcnk@{z_{2}}{k}\Jacobiellcnk@{z_{3}}{k}+\frac{1}{{k^{\prime}}^{2}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}\Jacobielldnk@{z_{2}}{k}\Jacobielldnk@{z_{3}}{k}</math>]] || <code>x = (k)^(2)* JacobiSN(z, k)*JacobiSN(z[1], k)*JacobiSN(z[2], k)*JacobiSN(z[3], k)-((k)^(2))/(1 - (k)^(2))*JacobiCN(z, k)*JacobiCN(z[1], k)*JacobiCN(z[2], k)*JacobiCN(z[3], k)+(1)/(1 - (k)^(2))*JacobiDN(z, k)*JacobiDN(z[1], k)*JacobiDN(z[2], k)*JacobiDN(z[3], k)</code> || <code>x = (k)^(2)* JacobiSN[z, (k)^2]*JacobiSN[Subscript[z, 1], (k)^2]*JacobiSN[Subscript[z, 2], (k)^2]*JacobiSN[Subscript[z, 3], (k)^2]-Divide[(k)^(2),1 - (k)^(2)]*JacobiCN[z, (k)^2]*JacobiCN[Subscript[z, 1], (k)^2]*JacobiCN[Subscript[z, 2], (k)^2]*JacobiCN[Subscript[z, 3], (k)^2]+Divide[1,1 - (k)^(2)]*JacobiDN[z, (k)^2]*JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2]</code> || Failure || Failure || Skip || Successful <br />
|-<br />
| [https://dlmf.nist.gov/29.8.E2 29.8.E2] || [[Item:Q8705|<math>\mu w(z_{1})w(z_{2})w(z_{3}) = \int_{-2\!\compellintKk@@{k}\!}^{2\!\compellintKk@@{k}\!}\FerrersP[]{\nu}@{x}w(z)\diff{z}</math>]] || <code>mu*w*(z[1])* w*(z[2])* w*(z[3])= int(LegendreP(nu, x)*w*(z), z = - 2*EllipticK(k)..2*EllipticK(k))</code> || <code>\[Mu]*w*(Subscript[z, 1])* w*(Subscript[z, 2])* w*(Subscript[z, 3])= Integrate[LegendreP[\[Nu], x]*w*(z), {z, - 2*EllipticK[(k)^2], 2*EllipticK[(k)^2]}]</code> || Failure || Failure || - || Skip <br />
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| [https://dlmf.nist.gov/29.8#Ex1 29.8#Ex1] || [[Item:Q8707|<math>w(z+2\!\compellintKk@@{k}\!) = \sigma w(z)</math>]] || <code>w*(z + 2*EllipticK(k))= sigma*w*(z)</code> || <code>w*(z + 2*EllipticK[(k)^2])= \[Sigma]*w*(z)</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[] <- {Rule[k, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[11.090638940207405, -2.3226169111049417] <- {Rule[k, 2], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[9.565752102125508, -2.5159784259617144] <- {Rule[k, 3], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>DirectedInfinity[] <- {Rule[k, 1], Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[σ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div> <br />
|-<br />
| [https://dlmf.nist.gov/29.8#Ex2 29.8#Ex2] || [[Item:Q8708|<math>w_{2}(z+2\!\compellintKk@@{k}\!) = \tau w(z)+\sigma w_{2}(z)</math>]] || <code>w[2]*(z + 2*EllipticK(k))= tau*w*(z)+ sigma*w[2]*(z)</code> || <code>Subscript[w, 2]*(z + 2*EllipticK[(k)^2])= \[Tau]*w*(z)+ \[Sigma]*Subscript[w, 2]*(z)</code> || Failure || Failure || Skip || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.8.E6 29.8.E6] || [[Item:Q8710|<math>y = \frac{1}{k^{\prime}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}</math>]] || <code>y =(1)/(sqrt(1 - (k)^(2)))*JacobiDN(z, k)*JacobiDN(z[1], k)</code> || <code>y =Divide[1,Sqrt[1 - (k)^(2)]]*JacobiDN[z, (k)^2]*JacobiDN[Subscript[z, 1], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 1, y = 3}</code><br><code>3.937738242+.2897798728*I <- {z = 2^(1/2)+I*2^(1/2), z[1] = 2^(1/2)+I*2^(1/2), k = 2, y = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>DirectedInfinity[] <- {Rule[k, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>DirectedInfinity[] <- {Rule[k, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>DirectedInfinity[] <- {Rule[k, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>DirectedInfinity[] <- {Rule[k, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div> <br />
|-<br />
| [https://dlmf.nist.gov/29.11.E1 29.11.E1] || [[Item:Q8721|<math>\deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0</math>]] || <code>diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2)+ (k)^(2)* (omega)^(2)* (JacobiSN(z, k))^(4))* w = 0</code> || <code>D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (k)^(2)* (\[Omega])^(2)* (JacobiSN[z, (k)^2])^(4))* w = 0</code> || Failure || Failure || Skip || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.14.E3 29.14.E3] || [[Item:Q8737|<math>w(s,t) = \Jacobiellsnk^{2}@{\!\compellintKk@@{k}\!+\iunit t}{k}-\Jacobiellsnk^{2}@{s}{k}</math>]] || <code>w*(s , t)= (JacobiSN(EllipticK(k)+ I*t, k))^(2)- (JacobiSN(s, k))^(2)</code> || <code>w*(s , t)= (JacobiSN[EllipticK[(k)^2]+ I*t, (k)^2])^(2)- (JacobiSN[s, (k)^2])^(2)</code> || Failure || Failure || Error || Error <br />
|-<br />
| [https://dlmf.nist.gov/29.17.E1 29.17.E1] || [[Item:Q8796|<math>F(z) = E(z)\int_{\iunit\!\ccompellintKk@@{k}\!}^{z}\frac{\diff{u}}{(E(u))^{2}}</math>]] || <code>F*(z)= E*(z)* int((1)/((E*(u))^(2)), u = I*EllipticCK(k)..z)</code> || <code>F*(z)= E*(z)* Integrate[Divide[1,(E*(u))^(2)], {u, I*EllipticK[1-(k)^2], z}]</code> || Failure || Failure || Skip || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Complex[0.03667157790603448, 4.331207863265408] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.11462120344581403, 4.482500644617256] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-0.2493650915526525, 4.6172445327240945] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[4.69908730443685, 0.33120786326540785] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[k, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div> <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex1 29.18#Ex1] || [[Item:Q8798|<math>x = kr\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</math>]] || <code>x = k*r*JacobiSN(beta, k)*JacobiSN(gamma, k)</code> || <code>x = k*r*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.2066406870-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 1}</code><br><code>1.206640687-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 2}</code><br><code>2.206640687-.8535459454*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, x = 3}</code><br><code>.9014522664-2.018283670*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 2, x = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex2 29.18#Ex2] || [[Item:Q8799|<math>y = \iunit\frac{k}{k^{\prime}}r\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</math>]] || <code>y = I*(k)/(sqrt(1 - (k)^(2)))*r*JacobiCN(beta, k)*JacobiCN(gamma, k)</code> || <code>y = I*Divide[k,Sqrt[1 - (k)^(2)]]*r*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 1, y = 3}</code><br><code>3.451665915+.7621257589*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), k = 2, y = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex3 29.18#Ex3] || [[Item:Q8800|<math>z = \frac{1}{k^{\prime}}r\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</math>]] || <code>z =(1)/(sqrt(1 - (k)^(2)))*r*JacobiDN(beta, k)*JacobiDN(gamma, k)</code> || <code>z =Divide[1,Sqrt[1 - (k)^(2)]]*r*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>1.356638323+2.584421950*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>1.490898086+1.415864964*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {beta = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex7 29.18#Ex7] || [[Item:Q8804|<math>0 <= \gamma</math>]] || <code>0 < = gamma</code> || <code>0 < = \[Gamma]</code> || Failure || Failure || Successful || Successful <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex7 29.18#Ex7] || [[Item:Q8804|<math>\gamma <= 4\!\compellintKk@@{k}\!</math>]] || <code>gamma < = 4*EllipticK(k)</code> || <code>\[Gamma]< = 4*EllipticK[(k)^2]</code> || Failure || Failure || Error || Successful <br />
|-<br />
| [https://dlmf.nist.gov/29.18.E5 29.18.E5] || [[Item:Q8806|<math>\deriv{}{r}\left(r^{2}\deriv{u_{1}}{r}\right)+(\omega^{2}r^{2}-\nu(\nu+1))u_{1} = 0</math>]] || <code>diff(((r)^(2)* diff(u[1], r))+((omega)^(2)* (r)^(2)- nu*(nu + 1))* u[1], r)= 0</code> || <code>D[((r)^(2)* D[Subscript[u, 1], r])+((\[Omega])^(2)* (r)^(2)- \[Nu]*(\[Nu]+ 1))* Subscript[u, 1], r]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-31.99999996+0.*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = 2^(1/2)+I*2^(1/2)}</code><br><code>0.+31.99999996*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = 2^(1/2)-I*2^(1/2)}</code><br><code>31.99999996+0.*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = -2^(1/2)-I*2^(1/2)}</code><br><code>0.-31.99999996*I <- {omega = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), u[1] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-32.0 <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, 32.0] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>32.0 <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[0.0, -32.0] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ω, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[u, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}</code><br>... skip entries to safe data<br></div></div> <br />
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| [https://dlmf.nist.gov/29.18.E6 29.18.E6] || [[Item:Q8807|<math>\deriv[2]{u_{2}}{\beta}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\beta}{k})u_{2} = 0</math>]] || <code>diff(u[2], [beta$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(beta, k))^(2))* u[2]= 0</code> || <code>D[Subscript[u, 2], {\[Beta], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Beta], (k)^2])^(2))* Subscript[u, 2]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>7.948739768-7.545139452*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>51.95468921+27.97388965*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>-3.910915794-11.82960931*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>-7.545139452-7.948739768*I <- {beta = 2^(1/2)+I*2^(1/2), h = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u[2] = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18.E7 29.18.E7] || [[Item:Q8808|<math>\deriv[2]{u_{3}}{\gamma}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\gamma}{k})u_{3} = 0</math>]] || <code>diff(u[3], [gamma$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(gamma, k))^(2))* u[3]= 0</code> || <code>D[Subscript[u, 3], {\[Gamma], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Gamma], (k)^2])^(2))* Subscript[u, 3]= 0</code> || Error || Failure || - || Skip <br />
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| [https://dlmf.nist.gov/29.18#Ex8 29.18#Ex8] || [[Item:Q8809|<math>x = k\Jacobiellsnk@{\alpha}{k}\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}</math>]] || <code>x = k*JacobiSN(alpha, k)*JacobiSN(beta, k)*JacobiSN(gamma, k)</code> || <code>x = k*JacobiSN[\[Alpha], (k)^2]*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>.3496751872-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 1}</code><br><code>1.349675187-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 2}</code><br><code>2.349675187-.4759618703e-1*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, x = 3}</code><br><code>.8887187920-1.136817507*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 2, x = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex9 29.18#Ex9] || [[Item:Q8810|<math>y = -\frac{k}{k^{\prime}}\Jacobiellcnk@{\alpha}{k}\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}</math>]] || <code>y = -(k)/(sqrt(1 - (k)^(2)))*JacobiCN(alpha, k)*JacobiCN(beta, k)*JacobiCN(gamma, k)</code> || <code>y = -Divide[k,Sqrt[1 - (k)^(2)]]*JacobiCN[\[Alpha], (k)^2]*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 1}</code><br><code>Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 2}</code><br><code>Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 1, y = 3}</code><br><code>-.314074508-.9043815133*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), k = 2, y = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/29.18#Ex10 29.18#Ex10] || [[Item:Q8811|<math>z = \frac{\iunit}{kk^{\prime}}\Jacobielldnk@{\alpha}{k}\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}</math>]] || <code>z =(I)/(k*sqrt(1 - (k)^(2)))*JacobiDN(alpha, k)*JacobiDN(beta, k)*JacobiDN(gamma, k)</code> || <code>z =Divide[I,k*Sqrt[1 - (k)^(2)]]*JacobiDN[\[Alpha], (k)^2]*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 1}</code><br><code>1.349197762+2.073332495*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 2}</code><br><code>1.413658462+1.427095902*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), k = 3}</code><br><code>Float(infinity)+Float(infinity)*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), k = 1}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
|}</div>
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