Results of Spheroidal Wave Functions

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DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
30.1#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S^{(1)}_{mn}(\gamma,0) = (-1)^{m}\FerrersP[m]{n}@{0}} (S[m*n])^(1)*(gamma , 0)=(- 1)^(m)* LegendreP(n, m, 0) (Subscript[S, m*n])^(1)*(\[Gamma], 0)=(- 1)^(m)* LegendreP[n, m, 0] Failure Failure Error Error
30.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(((1 - (z)^(2))*diff(w, z))+(lambda + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))* w, z)= 0 D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ (\[Gamma])^(2)*(1 - (z)^(2))-Divide[(\[Mu])^(2),1 - (z)^(2)])* w, z]= 0 Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
Fail
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]]]]}
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]]]]}
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]]]]}
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]]]]}
... skip entries to safe data
30.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(g, [t$(2)])+(lambda +(1)/(4)+ (gamma)^(2)* (sin(t))^(2)-((mu)^(2)-(1)/(4))/((sin(t))^(2)))* g = 0 D[g, {t, 2}]+(\[Lambda]+Divide[1,4]+ (\[Gamma])^(2)* (Sin[t])^(2)-Divide[(\[Mu])^(2)-Divide[1,4],(Sin[t])^(2)])* g = 0 Failure Failure
Fail
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)}
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)}
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)}
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)}
... skip entries to safe data
 Skip
30.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \cos@@{t}} z = cos(t) z = Cos[t] Failure Failure
Fail
1.074539570+3.325606671*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
1.074539570+.497179547*I <- {t = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-1.753887554+.497179547*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-1.753887554+3.325606671*I <- {t = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
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]]]]}
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]]]]}
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]]]]}
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]]]]}
... skip entries to safe data
30.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\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} ((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 ((\[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 Failure Failure
Fail
-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)}
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)}
-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)}
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)}
... skip entries to safe data
 Error
30.11#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{m}{3}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}+\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}} Error SpheroidalS3[n, m, z, \[Gamma]]= SpheroidalS1[n, m, z, \[Gamma]]+ I*SpheroidalS2[n, m, z, \[Gamma]] Error Failure - Skip
30.11#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{m}{4}{n}@{z}{\gamma} = \radsphwaveS{m}{1}{n}@{z}{\gamma}-\iunit\radsphwaveS{m}{2}{n}@{z}{\gamma}} Error SpheroidalS4[n, m, z, \[Gamma]]= SpheroidalS1[n, m, z, \[Gamma]]- I*SpheroidalS2[n, m, z, \[Gamma]] Error Failure - Skip
30.11.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Wronskian@{\radsphwaveS{m}{1}{n}@{z}{\gamma},\radsphwaveS{m}{2}{n}@{z}{\gamma}} = \frac{1}{\gamma(z^{2}-1)}} Error Wronskian[{SpheroidalS1[n, m, z, \[Gamma]], SpheroidalS2[n, m, z, \[Gamma]]}, z]=Divide[1,\[Gamma]*((z)^(2)- 1)] Error Failure - Skip
30.12.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(((1 - (z)^(2))*diff(w, z))+(lambda + alpha*z + (gamma)^(2)*(1 - (z)^(2))-((mu)^(2))/(1 - (z)^(2)))* w, z)= 0 D[((1 - (z)^(2))*D[w, z])+(\[Lambda]+ \[Alpha]*z + (\[Gamma])^(2)*(1 - (z)^(2))-Divide[(\[Mu])^(2),1 - (z)^(2)])* w, z]= 0 Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
 Skip
30.12.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} 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 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 Failure Failure
Fail
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)}
-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)}
-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)}
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)}
... skip entries to safe data
 Skip
30.13#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\cos@@{\phi}} x = c*sqrt(((xi)^(2)- 1)*(1 - (eta)^(2)))*cos(phi) x = c*Sqrt[((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2))]*Cos[\[Phi]] Failure Failure Skip Skip
30.13#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = c\sqrt{(\xi^{2}-1)(1-\eta^{2})}\sin@@{\phi}} y = c*sqrt(((xi)^(2)- 1)*(1 - (eta)^(2)))*sin(phi) y = c*Sqrt[((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2))]*Sin[\[Phi]] Failure Failure Skip Error
30.13.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\xi}^{2} = \left(\pderiv{x}{\xi}\right)^{2}+\left(\pderiv{y}{\xi}\right)^{2}+\left(\pderiv{z}{\xi}\right)^{2}} (h[xi])^(2)=(diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(z, xi))^(2) (Subscript[h, \[Xi]])^(2)=(D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[z, \[Xi]])^(2) Failure Failure
Fail
0.+3.999999998*I <- {h[xi] = 2^(1/2)+I*2^(1/2)}
0.-3.999999998*I <- {h[xi] = 2^(1/2)-I*2^(1/2)}
0.+3.999999998*I <- {h[xi] = -2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {h[xi] = -2^(1/2)+I*2^(1/2)}
 Error
30.13.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}} (diff(x, xi))^(2)+(diff(y, xi))^(2)+(diff(z, xi))^(2)=((c)^(2)*((xi)^(2)- (eta)^(2)))/((xi)^(2)- 1) (D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[z, \[Xi]])^(2)=Divide[(c)^(2)*((\[Xi])^(2)- (\[Eta])^(2)),(\[Xi])^(2)- 1] Failure Failure
Fail
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)}
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)}
-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)}
-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)}
... skip entries to safe data
 Error
30.13.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\eta}^{2} = \left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2}} (h[eta])^(2)=(diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(z, eta))^(2) (Subscript[h, \[Eta]])^(2)=(D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[z, \[Eta]])^(2) Failure Failure
Fail
0.+3.999999998*I <- {h[eta] = 2^(1/2)+I*2^(1/2)}
0.-3.999999998*I <- {h[eta] = 2^(1/2)-I*2^(1/2)}
0.+3.999999998*I <- {h[eta] = -2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {h[eta] = -2^(1/2)+I*2^(1/2)}
 Error
30.13.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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}}} (diff(x, eta))^(2)+(diff(y, eta))^(2)+(diff(z, eta))^(2)=((c)^(2)*((xi)^(2)- (eta)^(2)))/(1 - (eta)^(2)) (D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[z, \[Eta]])^(2)=Divide[(c)^(2)*((\[Xi])^(2)- (\[Eta])^(2)),1 - (\[Eta])^(2)] Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
 Error
30.13.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\phi}^{2} = \left(\pderiv{x}{\phi}\right)^{2}+\left(\pderiv{y}{\phi}\right)^{2}+\left(\pderiv{z}{\phi}\right)^{2}} (h[phi])^(2)=(diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(z, phi))^(2) (Subscript[h, \[Phi]])^(2)=(D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[z, \[Phi]])^(2) Failure Failure
Fail
0.+3.999999998*I <- {h[phi] = 2^(1/2)+I*2^(1/2)}
0.-3.999999998*I <- {h[phi] = 2^(1/2)-I*2^(1/2)}
0.+3.999999998*I <- {h[phi] = -2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {h[phi] = -2^(1/2)+I*2^(1/2)}
 Error
30.13.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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})} (diff(x, phi))^(2)+(diff(y, phi))^(2)+(diff(z, phi))^(2)= (c)^(2)*((xi)^(2)- 1)*(1 - (eta)^(2)) (D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[z, \[Phi]])^(2)= (c)^(2)*((\[Xi])^(2)- 1)*(1 - (\[Eta])^(2)) Failure Failure
Fail
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)}
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)}
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)}
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)}
... skip entries to safe data
 Error
30.13.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(((1 - (xi)^(2))*diff(w[1], xi))+(lambda + (gamma)^(2)*(1 - (xi)^(2))-((mu)^(2))/(1 - (xi)^(2)))* w[1], xi)= 0 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 Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
 Error
30.13.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(((1 - (eta)^(2))*diff(w[2], eta))+(lambda + (gamma)^(2)*(1 - (eta)^(2))-((mu)^(2))/(1 - (eta)^(2)))* w[2], eta)= 0 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 Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
 Error
30.13.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w_{3}}{\phi}+\mu^{2}w_{3} = 0} diff(w[3], [phi$(2)])+ (mu)^(2)* w[3]= 0 D[Subscript[w, 3], {\[Phi], 2}]+ (\[Mu])^(2)* Subscript[w, 3]= 0 Failure Failure
Fail
-5.656854245+5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = 2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = -2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {mu = 2^(1/2)+I*2^(1/2), w[3] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
 Error
30.13.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{3}(\phi) = a_{3}\cos@{m\phi}+b_{3}\sin@{m\phi}} w[3]*(phi)= a[3]*cos(m*phi)+ b[3]*sin(m*phi) Subscript[w, 3]*(\[Phi])= Subscript[a, 3]*Cos[m*\[Phi]]+ Subscript[b, 3]*Sin[m*\[Phi]] Failure Failure
Fail
-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}
-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}
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}
-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}
... skip entries to safe data
 Error
30.13.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{\xi}{\gamma}} Error Subscript[w, 1]*(\[Xi])= Subscript[a, 1]*SpheroidalS1[n, m, \[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, \[Xi], \[Gamma]] Error Failure - Error
30.13.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{m}{1}{n}@{\xi_{0}}{\gamma} = 0} Error SpheroidalS1[n, m, Subscript[\[Xi], 0], \[Gamma]]= 0 Error Failure - Error
30.14#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = c\sqrt{(\xi^{2}+1)(1-\eta^{2})}\cos@@{\phi}} x = c*sqrt(((xi)^(2)+ 1)*(1 - (eta)^(2)))*cos(phi) x = c*Sqrt[((\[Xi])^(2)+ 1)*(1 - (\[Eta])^(2))]*Cos[\[Phi]] Failure Failure
Fail
-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}
-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}
-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}
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}
... skip entries to safe data
 Error
30.14#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = c\sqrt{(\xi^{2}+1)(1-\eta^{2})}\sin@@{\phi}} y = c*sqrt(((xi)^(2)+ 1)*(1 - (eta)^(2)))*sin(phi) y = c*Sqrt[((\[Xi])^(2)+ 1)*(1 - (\[Eta])^(2))]*Sin[\[Phi]] Failure Failure
Fail
-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}
-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}
-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}
-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}
... skip entries to safe data
 Error
30.14.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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} diff(((1 + (xi)^(2))*diff(w[1], xi))-(lambda + (gamma)^(2)*(1 + (xi)^(2))-((mu)^(2))/(1 + (xi)^(2)))* w[1], xi)= 0 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 Failure Failure
Fail
-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)}
-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)}
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)}
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)}
... skip entries to safe data
 Error
30.14.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(\xi) = a_{1}\radsphwaveS{m}{1}{n}@{i\xi}{\gamma}+b_{1}\radsphwaveS{m}{2}{n}@{i\xi}{\gamma}} Error Subscript[w, 1]*(\[Xi])= Subscript[a, 1]*SpheroidalS1[n, m, I*\[Xi], \[Gamma]]+ Subscript[b, 1]*SpheroidalS2[n, m, I*\[Xi], \[Gamma]] Error Failure - Error
30.14.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{m}{1}{n}@{\iunit\xi_{0}}{\gamma} = 0} Error SpheroidalS1[n, m, I*Subscript[\[Xi], 0], \[Gamma]]= 0 Error Failure - Error
30.15.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\tau}^{\tau}\frac{\sin@@{\sigma(t-s)}}{\pi(t-s)}\phi_{n}(s)\diff{s} = \Lambda_{n}\phi_{n}(t)} int((sin(sigma*(t - s)))/(Pi*(t - s))*phi[n]*(s), s = - tau..tau)= Lambda[n]*phi[n]*(t) Integrate[Divide[Sin[\[Sigma]*(t - s)],Pi*(t - s)]*Subscript[\[Phi], n]*(s), {s, - \[Tau], \[Tau]}]= Subscript[\[CapitalLambda], n]*Subscript[\[Phi], n]*(t) Failure Failure Skip Error
30.15.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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)} 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) 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]) Failure Failure Skip Error
30.15.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \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)} 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) 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]) Failure Failure Skip Error
30.15.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\tau}^{\tau}\phi_{k}(t)\phi_{n}(t)\diff{t} = \Lambda_{n}\Kroneckerdelta{k}{n}} int(phi[k]*(t)* phi[n]*(t), t = - tau..tau)= Lambda[n]*KroneckerDelta[k, n] Integrate[Subscript[\[Phi], k]*(t)* Subscript[\[Phi], n]*(t), {t, - \[Tau], \[Tau]}]= Subscript[\[CapitalLambda], n]*KroneckerDelta[k, n] Failure Failure Skip Error
30.15.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{-\infty}^{\infty}\phi_{k}(t)\phi_{n}(t)\diff{t} = \Kroneckerdelta{k}{n}} int(phi[k]*(t)* phi[n]*(t), t = - infinity..infinity)= KroneckerDelta[k, n] Integrate[Subscript[\[Phi], k]*(t)* Subscript[\[Phi], n]*(t), {t, - Infinity, Infinity}]= KroneckerDelta[k, n] Failure Failure Skip Error
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