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Results of Spheroidal Wave Functions - Revision history
2024-03-28T15:44:22Z
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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 |- | [..."
2020-01-19T14:27:49Z
<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/30.1#Ex3 30.1#Ex3] || [[Item:Q8817|<math>S^{(1)}_{mn}(\gamma,0) = (-1)^{m}\FerrersP[m]{n}@{0}</math>]] || <code>(S[m*n])^(1)*(gamma , 0)=(- 1)^(m)* LegendreP(n, m, 0)</code> || <code>(Subscript[S, m*n])^(1)*(\[Gamma], 0)=(- 1)^(m)* LegendreP[n, m, 0]</code> || Failure || Failure || Error || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.2.E1 30.2.E1] || [[Item:Q8819|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</math>]] || <code>diff(((1 - (z)^(2))*diff(w, z))+(lambda + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))* w, z)= 0</code> || <code>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ (\[Gamma])^(2)*(1 - (z)^(2))-Divide[(\[Mu])^(2),1 - (z)^(2)])* w, z]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.660899653-1.779610239*I <- {mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.551236539+1.660899654*I <- {mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.660899653+1.779610239*I <- {mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.551236539-1.660899654*I <- {mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -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>Complex[30.33910034602076, 0.8858131487889274] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[33.660899653979236, -0.8858131487889274] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[30.33910034602076, 0.8858131487889274] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[33.660899653979236, -0.8858131487889274] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[γ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[μ, 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/30.2.E2 30.2.E2] || [[Item:Q8820|<math>\deriv[2]{g}{t}+\left(\lambda+\frac{1}{4}+\gamma^{2}\sin^{2}@@{t}-\frac{\mu^{2}-\frac{1}{4}}{\sin^{2}@@{t}}\right)g = 0</math>]] || <code>diff(g, [t$(2)])+(lambda +(1)/(4)+ (gamma)^(2)* (sin(t))^(2)-((mu)^(2)-(1)/(4))/((sin(t))^(2)))* g = 0</code> || <code>D[g, {t, 2}]+(\[Lambda]+Divide[1,4]+ (\[Gamma])^(2)* (Sin[t])^(2)-Divide[(\[Mu])^(2)-Divide[1,4],(Sin[t])^(2)])* g = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>2.795111666+5.673160258*I <- {g = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)+I*2^(1/2)}</code><br><code>4.636944094+5.150079117*I <- {g = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), t = 2^(1/2)-I*2^(1/2)}</code><br><code>2.795111666+5.673160258*I <- {g = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), t = -2^(1/2)-I*2^(1/2)}</code><br><code>4.636944094+5.150079117*I <- {g = 2^(1/2)+I*2^(1/2), lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), t = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.2#Ex1 30.2#Ex1] || [[Item:Q8821|<math>z = \cos@@{t}</math>]] || <code>z = cos(t)</code> || <code>z = Cos[t]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.074539570+3.325606671*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>1.074539570+.497179547*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.753887554+.497179547*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>-1.753887554+3.325606671*I <- {t = 2^(1/2)+I*2^(1/2), z = -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>Complex[1.0745395706783705, 3.3256066725373055] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[1.0745395706783705, 0.4971795477911152] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7538875540678198, 0.4971795477911152] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}</code><br><code>Complex[-1.7538875540678198, 3.3256066725373055] <- {Rule[t, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], 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/30.2.E4 30.2.E4] || [[Item:Q8823|<math>(\zeta^{2}-\gamma^{2})\deriv[2]{w}{\zeta}+2\zeta\deriv{w}{\zeta}+\left(\zeta^{2}-\lambda-\gamma^{2}-\frac{\gamma^{2}\mu^{2}}{\zeta^{2}-\gamma^{2}}\right)w = 0</math>]] || <code>((zeta)^(2)- (gamma)^(2))* diff(w, [zeta$(2)])+ 2*zeta*diff(w, zeta)+((zeta)^(2)- lambda - (gamma)^(2)-((gamma)^(2)* (mu)^(2))/((zeta)^(2)- (gamma)^(2)))* w = 0</code> || <code>((\[zeta])^(2)- (\[Gamma])^(2))* D[w, {\[zeta], 2}]+ 2*\[zeta]*D[w, \[zeta]]+((\[zeta])^(2)- \[Lambda]- (\[Gamma])^(2)-Divide[(\[Gamma])^(2)* (\[Mu])^(2),(\[zeta])^(2)- (\[Gamma])^(2)])* w = 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-6.634953849+.7567079812*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}</code><br><code>5.614631034-9.621124116*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}</code><br><code>-6.634953849+.7567079812*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}</code><br><code>5.614631034-9.621124116*I <- {lambda = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.11#Ex5 30.11#Ex5] || [[Item:Q8899|<math>\radsphwaveS{m}{3}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}+\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</math>]] || <code>Error</code> || <code>SpheroidalS3[n, m, z, \[Gamma]]= SpheroidalS1[n, m, z, \[Gamma]]+ I*SpheroidalS2[n, m, z, \[Gamma]]</code> || Error || Failure || - || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.11#Ex6 30.11#Ex6] || [[Item:Q8900|<math>\radsphwaveS{m}{4}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}-\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}</math>]] || <code>Error</code> || <code>SpheroidalS4[n, m, z, \[Gamma]]= SpheroidalS1[n, m, z, \[Gamma]]- I*SpheroidalS2[n, m, z, \[Gamma]]</code> || Error || Failure || - || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.11.E7 30.11.E7] || [[Item:Q8902|<math>\Wronskian@{\radsphwaveS{m}{1}{n}@{z}{\gamma},\radsphwaveS{m}{2}{n}@{z}{\gamma}} = \frac{1}{\gamma(z^{2}-1)}</math>]] || <code>Error</code> || <code>Wronskian[{SpheroidalS1[n, m, z, \[Gamma]], SpheroidalS2[n, m, z, \[Gamma]]}, z]=Divide[1,\[Gamma]*((z)^(2)- 1)]</code> || Error || Failure || - || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.12.E1 30.12.E1] || [[Item:Q8908|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+{\left(\lambda+\alpha z+\gamma^{2}(1-z^{2})-\frac{\mu^{2}}{1-z^{2}}\right)w} = 0</math>]] || <code>diff(((1 - (z)^(2))*diff(w, z))+(lambda + alpha*z + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))* w, z)= 0</code> || <code>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ \[Alpha]*z + (\[Gamma])^(2)*(1 - (z)^(2))-Divide[(\[Mu])^(2),1 - (z)^(2)])* w, z]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.660899654+2.220389759*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.551236539+5.660899652*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>1.660899655+5.779610238*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>3.551236538+2.339100344*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.12.E2 30.12.E2] || [[Item:Q8909|<math>\deriv{}{z}\left((1-z^{2})\deriv{w}{z}\right)+\left(\lambda+\gamma^{2}(1-z^{2})-\frac{\alpha(\alpha+1)}{z^{2}}-\frac{\mu^{2}}{1-z^{2}}\right)w = 0</math>]] || <code>diff(((1 - (z)^(2))*diff(w, z))+(lambda + (gamma)^(2)*(1 - (z)^(2))-(alpha*(alpha + 1))/((z)^(2))-((mu)^(2))/(1 - (z)^(2)))* w, z)= 0</code> || <code>D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ (\[Gamma])^(2)*(1 - (z)^(2))-Divide[\[Alpha]*(\[Alpha]+ 1),(z)^(2)]-Divide[(\[Mu])^(2),1 - (z)^(2)])* w, z]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.046207128-2.486717021*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}</code><br><code>-4.258343320-1.046207128*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.046207128+2.486717021*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}</code><br><code>4.258343320+1.046207128*I <- {alpha = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.13#Ex1 30.13#Ex1] || [[Item:Q8910|<math>x = c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\cos@@{\phi}</math>]] || <code>x = c*sqrt(((xi)^(2)- 1)*(1 - (eta)^(2)))*cos(phi)</code> || <code>x = c*Sqrt[((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2))]*Cos[\[Phi]]</code> || Failure || Failure || Skip || Skip <br />
|-<br />
| [https://dlmf.nist.gov/30.13#Ex2 30.13#Ex2] || [[Item:Q8911|<math>y = c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\sin@@{\phi}</math>]] || <code>y = c*sqrt(((xi)^(2)- 1)*(1 - (eta)^(2)))*sin(phi)</code> || <code>y = c*Sqrt[((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2))]*Sin[\[Phi]]</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E3 30.13.E3] || [[Item:Q8916|<math>h_{\xi}^{2} = \left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2}</math>]] || <code>(h[xi])^(2)=(diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(z, xi))^(2)</code> || <code>(Subscript[h, \[Xi]])^(2)=(D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[z, \[Xi]])^(2)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {h[xi] = 2^(1/2)+I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[xi] = 2^(1/2)-I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {h[xi] = -2^(1/2)-I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[xi] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E3 30.13.E3] || [[Item:Q8916|<math>\left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{\xi^{2}-1}</math>]] || <code>(diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(z, xi))^(2)=((c)^(2)*((xi)^(2)- (eta)^(2)))/((xi)^(2)- 1)</code> || <code>(D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[z, \[Xi]])^(2)=Divide[(c)^(2)*((\[Xi])^(2)- (\[Eta])^(2)),(\[Xi])^(2)- 1]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>-1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E4 30.13.E4] || [[Item:Q8917|<math>h_{\eta}^{2} = \left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2}</math>]] || <code>(h[eta])^(2)=(diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(z, eta))^(2)</code> || <code>(Subscript[h, \[Eta]])^(2)=(D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[z, \[Eta]])^(2)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {h[eta] = 2^(1/2)+I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[eta] = 2^(1/2)-I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {h[eta] = -2^(1/2)-I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[eta] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E4 30.13.E4] || [[Item:Q8917|<math>\left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2} = \frac{c^{2}(\xi^{2}-\eta^{2})}{1-\eta^{2}}</math>]] || <code>(diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(z, eta))^(2)=((c)^(2)*((xi)^(2)- (eta)^(2)))/(1 - (eta)^(2))</code> || <code>(D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[z, \[Eta]])^(2)=Divide[(c)^(2)*((\[Xi])^(2)- (\[Eta])^(2)),1 - (\[Eta])^(2)]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>-1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br><code>1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>1.882352941-7.529411761*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E5 30.13.E5] || [[Item:Q8918|<math>h_{\phi}^{2} = \left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2}</math>]] || <code>(h[phi])^(2)=(diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(z, phi))^(2)</code> || <code>(Subscript[h, \[Phi]])^(2)=(D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[z, \[Phi]])^(2)</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>0.+3.999999998*I <- {h[phi] = 2^(1/2)+I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[phi] = 2^(1/2)-I*2^(1/2)}</code><br><code>0.+3.999999998*I <- {h[phi] = -2^(1/2)-I*2^(1/2)}</code><br><code>0.-3.999999998*I <- {h[phi] = -2^(1/2)+I*2^(1/2)}</code><br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E5 30.13.E5] || [[Item:Q8918|<math>\left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2} = c^{2}(\xi^{2}-1)(1-\eta^{2})</math>]] || <code>(diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(z, phi))^(2)= (c)^(2)*((xi)^(2)- 1)*(1 - (eta)^(2))</code> || <code>(D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[z, \[Phi]])^(2)= (c)^(2)*((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2))</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>31.99999997-59.99999989*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)}</code><br><code>0.+67.99999989*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)}</code><br><code>31.99999997-59.99999989*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)}</code><br><code>0.+67.99999989*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E9 30.13.E9] || [[Item:Q8922|<math>\deriv{}{\xi}\left((1-\xi^{2})\deriv{w_{1}}{\xi}\right)+\left(\lambda+\gamma^{2}(1-\xi^{2})-\frac{\mu^{2}}{1-\xi^{2}}\right)w_{1} = 0</math>]] || <code>diff(((1 - (xi)^(2))*diff(w[1], xi))+(lambda + (gamma)^(2)*(1 - (xi)^(2))-((mu)^(2))/(1 - (xi)^(2)))* w[1], xi)= 0</code> || <code>D[((1 - (\[Xi])^(2))*D[Subscript[w, 1], \[Xi]])+(\[Lambda]+ (\[Gamma])^(2)*(1 - (\[Xi])^(2))-Divide[(\[Mu])^(2),1 - (\[Xi])^(2)])* Subscript[w, 1], \[Xi]]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.660899653-1.779610239*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.779610239+1.660899653*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.660899653+1.779610239*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.779610239-1.660899653*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E10 30.13.E10] || [[Item:Q8923|<math>\deriv{}{\eta}\left((1-\eta^{2})\deriv{w_{2}}{\eta}\right)+\left(\lambda+\gamma^{2}(1-\eta^{2})-\frac{\mu^{2}}{1-\eta^{2}}\right)w_{2} = 0</math>]] || <code>diff(((1 - (eta)^(2))*diff(w[2], eta))+(lambda + (gamma)^(2)*(1 - (eta)^(2))-((mu)^(2))/(1 - (eta)^(2)))* w[2], eta)= 0</code> || <code>D[((1 - (\[Eta])^(2))*D[Subscript[w, 2], \[Eta]])+(\[Lambda]+ (\[Gamma])^(2)*(1 - (\[Eta])^(2))-Divide[(\[Mu])^(2),1 - (\[Eta])^(2)])* Subscript[w, 2], \[Eta]]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.660899653-1.779610239*I <- {eta = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w[2] = 2^(1/2)+I*2^(1/2)}</code><br><code>-1.779610239+1.660899653*I <- {eta = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w[2] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.660899653+1.779610239*I <- {eta = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w[2] = -2^(1/2)-I*2^(1/2)}</code><br><code>1.779610239-1.660899653*I <- {eta = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), w[2] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E11 30.13.E11] || [[Item:Q8924|<math>\deriv[2]{w_{3}}{\phi}+\mu^{2}w_{3} = 0</math>]] || <code>diff(w[3], [phi$(2)])+ (mu)^(2)* w[3]= 0</code> || <code>D[Subscript[w, 3], {\[Phi], 2}]+ (\[Mu])^(2)* Subscript[w, 3]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-5.656854245+5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)+I*2^(1/2)}</code><br><code>5.656854245+5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)-I*2^(1/2)}</code><br><code>5.656854245-5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = -2^(1/2)-I*2^(1/2)}</code><br><code>-5.656854245-5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E12 30.13.E12] || [[Item:Q8925|<math>w_{3}(\phi) = a_{3}\cos@{m\phi}+b_{3}\sin@{m\phi}</math>]] || <code>w[3]*(phi)= a[3]*cos(m*phi)+ b[3]*sin(m*phi)</code> || <code>Subscript[w, 3]*(\[Phi])= Subscript[a, 3]*Cos[m*\[Phi]]+ Subscript[b, 3]*Sin[m*\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-5.799465200+2.753260584*I <- {phi = 2^(1/2)+I*2^(1/2), a[3] = 2^(1/2)+I*2^(1/2), b[3] = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)+I*2^(1/2), m = 1}</code><br><code>-7.291659687+26.73735930*I <- {phi = 2^(1/2)+I*2^(1/2), a[3] = 2^(1/2)+I*2^(1/2), b[3] = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)+I*2^(1/2), m = 2}</code><br><code>87.76595466+48.56777479*I <- {phi = 2^(1/2)+I*2^(1/2), a[3] = 2^(1/2)+I*2^(1/2), b[3] = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)+I*2^(1/2), m = 3}</code><br><code>-1.799465202-1.246739414*I <- {phi = 2^(1/2)+I*2^(1/2), a[3] = 2^(1/2)+I*2^(1/2), b[3] = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)-I*2^(1/2), m = 1}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E14 30.13.E14] || [[Item:Q8927|<math>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{\xi}{\gamma}</math>]] || <code>Error</code> || <code>Subscript[w, 1]*(\[Xi])= Subscript[a, 1]*SpheroidalS1[n, m, \[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, \[Xi], \[Gamma]]</code> || Error || Failure || - || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.13.E15 30.13.E15] || [[Item:Q8928|<math>\radsphwaveS{m}{1}{n}@{\xi_{0}}{\gamma} = 0</math>]] || <code>Error</code> || <code>SpheroidalS1[n, m, Subscript[\[Xi], 0], \[Gamma]]= 0</code> || Error || Failure || - || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.14#Ex1 30.14#Ex1] || [[Item:Q8930|<math>x = c\sqrt{(\xi^{2}+1)(1-\eta^{2})}\cos@@{\phi}</math>]] || <code>x = c*sqrt(((xi)^(2)+ 1)*(1 - (eta)^(2)))*cos(phi)</code> || <code>x = c*Sqrt[((\[Xi])^(2)+ 1)*(1 - (\[Eta])^(2))]*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-12.12586397+9.164618552*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 1}</code><br><code>-11.12586397+9.164618552*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 2}</code><br><code>-10.12586397+9.164618552*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), x = 3}</code><br><code>6.707496333+14.95670498*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), x = 1}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.14#Ex2 30.14#Ex2] || [[Item:Q8931|<math>y = c\sqrt{(\xi^{2}+1)(1-\eta^{2})}\sin@@{\phi}</math>]] || <code>y = c*sqrt(((xi)^(2)+ 1)*(1 - (eta)^(2)))*sin(phi)</code> || <code>y = c*Sqrt[((\[Xi])^(2)+ 1)*(1 - (\[Eta])^(2))]*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-9.78594361-14.30505684*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 1}</code><br><code>-8.78594361-14.30505684*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 2}</code><br><code>-7.78594361-14.30505684*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), y = 3}</code><br><code>-15.49391918+6.994416394*I <- {c = 2^(1/2)+I*2^(1/2), eta = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2), y = 1}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.14.E7 30.14.E7] || [[Item:Q8940|<math>\deriv{}{\xi}\left((1+\xi^{2})\deriv{w_{1}}{\xi}\right)-\left(\lambda+\gamma^{2}(1+\xi^{2})-\frac{\mu^{2}}{1+\xi^{2}}\right)w_{1} = 0</math>]] || <code>diff(((1 + (xi)^(2))*diff(w[1], xi))-(lambda + (gamma)^(2)*(1 + (xi)^(2))-((mu)^(2))/(1 + (xi)^(2)))* w[1], xi)= 0</code> || <code>D[((1 + (\[Xi])^(2))*D[Subscript[w, 1], \[Xi]])-(\[Lambda]+ (\[Gamma])^(2)*(1 + (\[Xi])^(2))-Divide[(\[Mu])^(2),1 + (\[Xi])^(2)])* Subscript[w, 1], \[Xi]]= 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Fail<div class="mw-collapsible-content"><code>-1.660899654-3.551236539*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = 2^(1/2)+I*2^(1/2)}</code><br><code>-3.551236539+1.660899654*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = 2^(1/2)-I*2^(1/2)}</code><br><code>1.660899654+3.551236539*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = -2^(1/2)-I*2^(1/2)}</code><br><code>3.551236539-1.660899654*I <- {mu = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2), w[1] = -2^(1/2)+I*2^(1/2)}</code><br>... skip entries to safe data<br></div></div> || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.14.E8 30.14.E8] || [[Item:Q8941|<math>w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{i\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{i\xi}{\gamma}</math>]] || <code>Error</code> || <code>Subscript[w, 1]*(\[Xi])= Subscript[a, 1]*SpheroidalS1[n, m, I*\[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, I*\[Xi], \[Gamma]]</code> || Error || Failure || - || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.14.E9 30.14.E9] || [[Item:Q8942|<math>\radsphwaveS{m}{1}{n}@{\iunit\xi_{0}}{\gamma} = 0</math>]] || <code>Error</code> || <code>SpheroidalS1[n, m, I*Subscript[\[Xi], 0], \[Gamma]]= 0</code> || Error || Failure || - || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.15.E3 30.15.E3] || [[Item:Q8945|<math>\int_{-\tau}^{\tau}\frac{\sin@@{\sigma(t-s)}}{\pi(t-s)}\phi_{n}(s)\diff{s} = \Lambda_{n}\phi_{n}(t)</math>]] || <code>int((sin(sigma*(t - s)))/(Pi*(t - s))*phi[n]*(s), s = - tau..tau)= Lambda[n]*phi[n]*(t)</code> || <code>Integrate[Divide[Sin[\[Sigma]*(t - s)],Pi*(t - s)]*Subscript[\[Phi], n]*(s), {s, - \[Tau], \[Tau]}]= Subscript[\[CapitalLambda], n]*Subscript[\[Phi], n]*(t)</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.15.E4 30.15.E4] || [[Item:Q8946|<math>\int_{-\infty}^{\infty}e^{-\iunit t\omega}\phi_{n}(t)\diff{t} = (-\iunit)^{n}\sqrt{\frac{2\pi\tau}{\sigma\Lambda_{n}}}\phi_{n}\left(\frac{\tau}{\sigma}\omega\right)\chi_{\sigma}(\omega)</math>]] || <code>int(exp(- I*t*omega)*phi[n]*(t), t = - infinity..infinity)=(- I)^(n)*sqrt((2*Pi*tau)/(sigma*Lambda[n]))*phi[n]*((tau)/(sigma)*omega)* chi[sigma]*(omega)</code> || <code>Integrate[Exp[- I*t*\[Omega]]*Subscript[\[Phi], n]*(t), {t, - Infinity, Infinity}]=(- I)^(n)*Sqrt[Divide[2*Pi*\[Tau],\[Sigma]*Subscript[\[CapitalLambda], n]]]*Subscript[\[Phi], n]*(Divide[\[Tau],\[Sigma]]*\[Omega])* Subscript[\[Chi], \[Sigma]]*(\[Omega])</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.15.E5 30.15.E5] || [[Item:Q8947|<math>\int_{-\tau}^{\tau}e^{-\iunit t\omega}\phi_{n}(t)\diff{t} = (-\iunit)^{n}\sqrt{\frac{2\pi\tau\Lambda_{n}}{\sigma}}\phi_{n}\left(\frac{\tau}{\sigma}\omega\right)</math>]] || <code>int(exp(- I*t*omega)*phi[n]*(t), t = - tau..tau)=(- I)^(n)*sqrt((2*Pi*tau*Lambda[n])/(sigma))*phi[n]*((tau)/(sigma)*omega)</code> || <code>Integrate[Exp[- I*t*\[Omega]]*Subscript[\[Phi], n]*(t), {t, - \[Tau], \[Tau]}]=(- I)^(n)*Sqrt[Divide[2*Pi*\[Tau]*Subscript[\[CapitalLambda], n],\[Sigma]]]*Subscript[\[Phi], n]*(Divide[\[Tau],\[Sigma]]*\[Omega])</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.15.E7 30.15.E7] || [[Item:Q8949|<math>\int_{-\tau}^{\tau}\phi_{k}(t)\phi_{n}(t)\diff{t} = \Lambda_{n}\Kroneckerdelta{k}{n}</math>]] || <code>int(phi[k]*(t)* phi[n]*(t), t = - tau..tau)= Lambda[n]*KroneckerDelta[k, n]</code> || <code>Integrate[Subscript[\[Phi], k]*(t)* Subscript[\[Phi], n]*(t), {t, - \[Tau], \[Tau]}]= Subscript[\[CapitalLambda], n]*KroneckerDelta[k, n]</code> || Failure || Failure || Skip || Error <br />
|-<br />
| [https://dlmf.nist.gov/30.15.E8 30.15.E8] || [[Item:Q8950|<math>\int_{-\infty}^{\infty}\phi_{k}(t)\phi_{n}(t)\diff{t} = \Kroneckerdelta{k}{n}</math>]] || <code>int(phi[k]*(t)* phi[n]*(t), t = - infinity..infinity)= KroneckerDelta[k, n]</code> || <code>Integrate[Subscript[\[Phi], k]*(t)* Subscript[\[Phi], n]*(t), {t, - Infinity, Infinity}]= KroneckerDelta[k, n]</code> || Failure || Failure || Skip || Error <br />
|-<br />
|}</div>
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