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] Error Failure - 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
Failed [260 / 300]
260/300]: [[.6668220767+1.154969718*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
1.154431362-.6665112581*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[2.0, 2.220446049250313*^-16] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-2.220446049250313*^-16, -3.4641016151377553] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[1.221198255+.2773804949*I <- {g = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = -3/2}
1.221198255+.2773804949*I <- {g = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, t = 3/2}
Failed [300 / 300]
{Complex[0.9341014939589334, 1.1066213513350005] <- {Rule[g, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.9341014939589334, 3.116679181619939] <- {Rule[g, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [42 / 42]
42/42]: [[.7952882023+.5000000000*I <- {t = -3/2, z = 1/2*3^(1/2)+1/2*I}
-.5707372017+.8660254040*I <- {t = -3/2, z = -1/2+1/2*I*3^(1/2)}
Failed [42 / 42]
{Complex[0.7952882021167358, 0.49999999999999994] <- {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5707372016677027, 0.8660254037844387] <- {Rule[t, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[-1.159496529-.1040714462*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I}
-.5887458836-1.840397716*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, zeta = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
DirectedInfinity[] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
30.3#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{k} = \gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)}} alpha[k] = (gamma)^(2)*((k + 2*m + 1)*(k + 2*m + 2))/((2*k + 2*m + 3)*(2*k + 2*m + 5)) Subscript[\[Alpha], k] == \[Gamma]^(2)*Divide[(k + 2*m + 1)*(k + 2*m + 2),(2*k + 2*m + 3)*(2*k + 2*m + 5)] Skipped - no semantic math Skipped - no semantic math - -
30.3#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{k} = (k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k+2m+3)}} beta[k] = (k + m)*(k + m + 1)- 2*(gamma)^(2)*((k + m)*(k + m + 1)- 1 + (m)^(2))/((2*k + 2*m - 1)*(2*k + 2*m + 3)) Subscript[\[Beta], k] == (k + m)*(k + m + 1)- 2*\[Gamma]^(2)*Divide[(k + m)*(k + m + 1)- 1 + (m)^(2),(2*k + 2*m - 1)*(2*k + 2*m + 3)] Skipped - no semantic math Skipped - no semantic math - -
30.3#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{k} = \gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}} gamma[k] = (gamma)^(2)*((k - 1)* k)/((2*k + 2*m - 3)*(2*k + 2*m - 1)) Subscript[\[Gamma], k] == \[Gamma]^(2)*Divide[(k - 1)* k,(2*k + 2*m - 3)*(2*k + 2*m - 1)] Skipped - no semantic math Skipped - no semantic math - -
30.3#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell_{0} = n(n+1)} ell[0] = n*(n + 1) Subscript[\[ScriptL], 0] == n*(n + 1) Skipped - no semantic math Skipped - no semantic math - -
30.3#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\ell_{2} = -1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)}} 2*ell[2] = - 1 -((2*m - 1)*(2*m + 1))/((2*n - 1)*(2*n + 3)) 2*Subscript[\[ScriptL], 2] == - 1 -Divide[(2*m - 1)*(2*m + 1),(2*n - 1)*(2*n + 3)] Skipped - no semantic math Skipped - no semantic math - -
30.3#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\ell_{4} = \frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}} 2*ell[4] = ((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 3)*(2*n - 1)^(3)*(2*n + 1))-((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n + 1)*(2*n + 3)^(3)*(2*n + 5)) 2*Subscript[\[ScriptL], 4] == Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 3)*(2*n - 1)^(3)*(2*n + 1)]-Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n + 1)*(2*n + 3)^(3)*(2*n + 5)] Skipped - no semantic math Skipped - no semantic math - -
30.3.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell_{6} = (4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right)} ell[6] = (4*(m)^(2)- 1)*(((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7))-((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3))) Subscript[\[ScriptL], 6] == (4*(m)^(2)- 1)*(Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7)]-Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3)]) Skipped - no semantic math Skipped - no semantic math - -
30.3.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell_{8} = 2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D} ell[8] = 2*(4*(m)^(2)- 1)^(2)* A +(1)/(16)*B +(1)/(8)*C +(1)/(2)*D Subscript[\[ScriptL], 8] == 2*(4*(m)^(2)- 1)^(2)* A +Divide[1,16]*B +Divide[1,8]*C +Divide[1,2]*D Skipped - no semantic math Skipped - no semantic math - -
30.8.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=-R}^{\infty}a_{n,k}^{m}(\gamma^{2})a_{n,k}^{-m}(\gamma^{2})\frac{1}{2n+4k+1} = \frac{1}{2n+1}} sum(a(a[n , k])^(m)*((gamma)^(2))* a(a[n , k])^(- m)*((gamma)^(2))*(1)/(2*n + 4*k + 1), k = - R..infinity) = (1)/(2*n + 1) Sum[a(Subscript[a, n , k])^(m)*(\[Gamma]^(2))* a(Subscript[a, n , k])^(- m)*(\[Gamma]^(2))*Divide[1,2*n + 4*k + 1], {k, - R, Infinity}, GenerateConditions->None] == Divide[1,2*n + 1] Skipped - no semantic math Skipped - no semantic math - -
30.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n,k}^{-m}(\gamma^{2}) = \frac{(n-m)!(n+m+2k)!}{(n+m)!(n-m+2k)!}a_{n,k}^{m}(\gamma^{2})} (a[n , k])^(- m)*((gamma)^(2)) = (factorial(n - m)*factorial(n + m + 2*k))/(factorial(n + m)*factorial(n - m + 2*k))*(a[n , k])^(m)*((gamma)^(2)) (Subscript[a, n , k])^(- m)*(\[Gamma]^(2)) == Divide[(n - m)!*(n + m + 2*k)!,(n + m)!*(n - m + 2*k)!]*(Subscript[a, n , k])^(m)*(\[Gamma]^(2)) Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{16}\beta_{4} = -63q^{6}-4940q^{4}-43327q^{2}-22470+128m^{2}(115q^{4}+1310q^{2}+735)-24576m^{4}(q^{2}+1)} (2)^(16)* beta[4] = - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1) (2)^(16)* Subscript[\[Beta], 4] == - 63*(q)^(6)- 4940*(q)^(4)- 43327*(q)^(2)- 22470 + 128*(m)^(2)*(115*(q)^(4)+ 1310*(q)^(2)+ 735)- 24576*(m)^(4)*((q)^(2)+ 1) Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{20}\beta_{5} = -527q^{7}-61529q^{5}-10\;43961q^{3}-22\;41599q+32m^{2}(5739q^{5}+1\;27550q^{3}+2\;98951q)-2048m^{4}(355q^{3}+1505q)+65536m^{6}q} (2)^(20)* beta[5] = - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q (2)^(20)* Subscript[\[Beta], 5] == - 527*(q)^(7)- 61529*(q)^(5)- 1043961*(q)^(3)- 2241599*q + 32*(m)^(2)*(5739*(q)^(5)+ 127550*(q)^(3)+ 298951*q)- 2048*(m)^(4)*(355*(q)^(3)+ 1505*q)+ 65536*(m)^(6)* q Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2c_{0} = -q^{2}-1+m^{2}} 2*c[0] = - (q)^(2)- 1 + (m)^(2) 2*Subscript[c, 0] == - (q)^(2)- 1 + (m)^(2) Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8c_{1} = -q^{3}-q+m^{2}q} 8*c[1] = - (q)^(3)- q + (m)^(2)* q 8*Subscript[c, 1] == - (q)^(3)- q + (m)^(2)* q Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{6}c_{2} = -5q^{4}-10q^{2}-1+2m^{2}(3q^{2}+1)-m^{4}} (2)^(6)* c[2] = - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4) (2)^(6)* Subscript[c, 2] == - 5*(q)^(4)- 10*(q)^(2)- 1 + 2*(m)^(2)*(3*(q)^(2)+ 1)- (m)^(4) Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{9}c_{3} = -33q^{5}-114q^{3}-37q+2m^{2}(23q^{3}+25q)-13m^{4}q} (2)^(9)* c[3] = - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q (2)^(9)* Subscript[c, 3] == - 33*(q)^(5)- 114*(q)^(3)- 37*q + 2*(m)^(2)*(23*(q)^(3)+ 25*q)- 13*(m)^(4)* q Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{10}c_{4} = -63q^{6}-340q^{4}-239q^{2}-14+10m^{2}(10q^{4}+23q^{2}+3)-3m^{4}(13q^{2}+6)+2m^{6}} (2)^(10)* c[4] = - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6) (2)^(10)* Subscript[c, 4] == - 63*(q)^(6)- 340*(q)^(4)- 239*(q)^(2)- 14 + 10*(m)^(2)*(10*(q)^(4)+ 23*(q)^(2)+ 3)- 3*(m)^(4)*(13*(q)^(2)+ 6)+ 2*(m)^(6) Skipped - no semantic math Skipped - no semantic math - -
30.9#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{13}c_{5} = -527q^{7}-4139q^{5}-5221q^{3}-1009q+m^{2}(939q^{5}+3750q^{3}+1591q)-m^{4}(465q^{3}+635q)+53m^{6}q} (2)^(13)* c[5] = - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q (2)^(13)* Subscript[c, 5] == - 527*(q)^(7)- 4139*(q)^(5)- 5221*(q)^(3)- 1009*q + (m)^(2)*(939*(q)^(5)+ 3750*(q)^(3)+ 1591*q)- (m)^(4)*(465*(q)^(3)+ 635*q)+ 53*(m)^(6)* q Skipped - no semantic math Skipped - no semantic math - -
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]] Missing Macro Error Failure - Skipped - Because timed out
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]] Missing Macro Error Failure - Skipped - Because timed out
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)] Missing Macro Error Failure - Error
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
Failed [300 / 300]
300/300]: [[1.965860183+1.904969718*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
2.453469468+.8348874183e-1*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[3.299038105676658, 0.7500000000000002] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.2990381056766578, -2.7141016151377553] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[4.416822075-5.340220804*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
7.649621884+3.083488740*I <- {alpha = 3/2, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[5.749999999999999, -6.495190528383291] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.749999999999999, -9.959292143521045] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
30.13#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1 < \xi} 1 < xi 1 < \[Xi] Skipped - no semantic math Skipped - no semantic math - -
30.13#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 < \eta} - 1 < eta - 1 < \[Eta] Skipped - no semantic math Skipped - no semantic math - -
30.13#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \phi} 0 <= phi 0 <= \[Phi] Skipped - no semantic math Skipped - no semantic math - -
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(x + y*I, xi))^(2) (Subscript[h, \[Xi]])^(2) == (D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[x + y*I, \[Xi]])^(2) Failure Failure
Failed [300 / 300]
300/300]: [[.5000000004+.8660254040*I <- {x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2, h[xi] = 1/2*3^(1/2)+1/2*I}
-.5000000004-.8660254040*I <- {x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2, h[xi] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ξ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.4999999999999998, -0.8660254037844387] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ξ], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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(x + y*I, xi))^(2) = ((c)^(2)*((xi)^(2)- (eta)^(2)))/((xi)^(2)- 1) (D[x, \[Xi]])^(2)+(D[y, \[Xi]])^(2)+(D[x + y*I, \[Xi]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)- \[Eta]^(2)),\[Xi]^(2)- 1] Failure Failure
Failed [240 / 300]
240/300]: [[-2.250000002-1.299038105*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = -3/2}
-2.250000002-1.299038105*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = 3/2}
Failed [240 / 300]
{Complex[-2.25, -1.2990381056766578] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-2.25, -1.2990381056766578] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
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(x + y*I, eta))^(2) (Subscript[h, \[Eta]])^(2) == (D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[x + y*I, \[Eta]])^(2) Failure Failure
Failed [300 / 300]
300/300]: [[.5000000004+.8660254040*I <- {eta = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[eta] = 1/2*3^(1/2)+1/2*I}
-.5000000004-.8660254040*I <- {eta = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[eta] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, η], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.4999999999999998, -0.8660254037844387] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, η], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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(x + y*I, eta))^(2) = ((c)^(2)*((xi)^(2)- (eta)^(2)))/(1 - (eta)^(2)) (D[x, \[Eta]])^(2)+(D[y, \[Eta]])^(2)+(D[x + y*I, \[Eta]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)- \[Eta]^(2)),1 - \[Eta]^(2)] Failure Failure
Failed [240 / 300]
240/300]: [[-2.250000002+3.897114318*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = -3/2}
-2.250000002+3.897114318*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = -1/2+1/2*I*3^(1/2), y = 3/2}
Failed [240 / 300]
{Complex[-2.2500000000000004, 3.897114317029973] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
Complex[-2.2500000000000004, 3.897114317029973] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
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(x + y*I, phi))^(2) (Subscript[h, \[Phi]])^(2) == (D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[x + y*I, \[Phi]])^(2) Failure Failure
Failed [300 / 300]
300/300]: [[.5000000004+.8660254040*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[phi] = 1/2*3^(1/2)+1/2*I}
-.5000000004-.8660254040*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, h[phi] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ϕ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.4999999999999998, -0.8660254037844387] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[h, ϕ], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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(x + y*I, phi))^(2) = (c)^(2)*((xi)^(2)- 1)*(1 - (eta)^(2)) (D[x, \[Phi]])^(2)+(D[y, \[Phi]])^(2)+(D[x + y*I, \[Phi]])^(2) == (c)^(2)*(\[Xi]^(2)- 1)*(1 - \[Eta]^(2)) Failure Failure
Failed [300 / 300]
300/300]: [[-1.125000002-1.948557157*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = -3/2}
-1.125000002-1.948557157*I <- {c = -3/2, eta = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, y = 3/2}
Failed [300 / 300]
{Complex[-1.125, -1.9485571585149866] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-1.125, -1.9485571585149866] <- {Rule[c, -1.5], Rule[x, 1.5], Rule[y, -1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
30.13.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{h_{\xi}h_{\eta}h_{\phi}}\left(\pderiv{}{\xi}\left(\frac{h_{\eta}h_{\phi}}{h_{\xi}}\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left(\frac{h_{\xi}h_{\phi}}{h_{\eta}}\pderiv{}{\eta}\right)+\pderiv{}{\phi}\left(\frac{h_{\xi}h_{\eta}}{h_{\phi}}\pderiv{}{\phi}\right)\right) = \frac{1}{c^{2}(\xi^{2}-\eta^{2})}\left(\pderiv{}{\xi}\left((\xi^{2}-1)\pderiv{}{\xi}\right)+\pderiv{}{\eta}\left((1-\eta^{2})\pderiv{}{\eta}\right)+\frac{\xi^{2}-\eta^{2}}{(\xi^{2}-1)(1-\eta^{2})}\pderiv[2]{}{\phi}\right)} (diff((((xi)^(2)- 1)*diff((1)/((c)^(2)*((xi)^(2)- (eta)^(2)))*((xi)^(2)- 1), xi))+ diff(diff(((1 - (eta)^(2))*diff((diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ diff(((h[xi]*h[phi])/(h[eta])*diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ (h[xi]*h[phi])/(h[eta]), eta))+ diff((h[xi]*h[eta])/(h[phi])*diff(((h[xi]*h[phi])/(h[eta])*diff(((h[eta]*h[phi])/(h[xi])*diff((1)/(h[xi]*h[eta]*h[phi])*(h[eta]*h[phi])/(h[xi]), xi))+ (h[xi]*h[phi])/(h[eta]), eta))+ (h[xi]*h[eta])/(h[phi]), phi), phi), eta), xi)) (((xi)^(2)- 1)*diff((1)/((c)^(2)*((xi)^(2)- (eta)^(2)))*((xi)^(2)- 1), xi))+ (1 - (eta)^(2)), eta))+((xi)^(2)- (eta)^(2))/(((xi)^(2)- 1)*(1 - (eta)^(2))), [phi$(2)]), eta), xi)) (D[((\[Xi]^(2)- 1)*D[Divide[1,(c)^(2)*(\[Xi]^(2)- \[Eta]^(2))]*(\[Xi]^(2)- 1), \[Xi]])+ D[D[((1 - \[Eta]^(2))*D[(D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ D[(Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]]*D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]], \[Eta]])+ D[Divide[Subscript[h, \[Xi]]*Subscript[h, \[Eta]],Subscript[h, \[Phi]]]*D[(Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]]*D[(Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]]*D[Divide[1,Subscript[h, \[Xi]]*Subscript[h, \[Eta]]*Subscript[h, \[Phi]]]*Divide[Subscript[h, \[Eta]]*Subscript[h, \[Phi]],Subscript[h, \[Xi]]], \[Xi]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Phi]],Subscript[h, \[Eta]]], \[Eta]])+ Divide[Subscript[h, \[Xi]]*Subscript[h, \[Eta]],Subscript[h, \[Phi]]], \[Phi]], \[Phi]], \[Eta]], \[Xi]]) ((\[Xi]^(2)- 1)*D[Divide[1,(c)^(2)*(\[Xi]^(2)- \[Eta]^(2))]*(\[Xi]^(2)- 1), \[Xi]])+ (1 - \[Eta]^(2)), \[Eta]])+Divide[\[Xi]^(2)- \[Eta]^(2),(\[Xi]^(2)- 1)*(1 - \[Eta]^(2))], {\[Phi], 2}], \[Eta]], \[Xi]]) Translation Error Translation Error - -
30.13.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(\xi,\eta,\phi) = w_{1}(\xi)w_{2}(\eta)w_{3}(\phi)} w*(xi , eta , phi) = w[1]*(xi)* w[2]*(eta)* w[3]*(phi) w*(\[Xi], \[Eta], \[Phi]) == Subscript[w, 1]*(\[Xi])* Subscript[w, 2]*(\[Eta])* Subscript[w, 3]*(\[Phi]) Skipped - no semantic math Skipped - no semantic math - -
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
Failed [260 / 300]
260/300]: [[.6668220767+1.154969718*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I}
-1.154969718+.6668220767*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[2.0, 2.220446049250313*^-16] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, 1.9999999999999998] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[.6668220767+1.154969718*I <- {eta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I}
-1.154969718+.6668220767*I <- {eta = 1/2*3^(1/2)+1/2*I, gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, w[2] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[2.0, 2.220446049250313*^-16] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, 1.9999999999999998] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[.3233738859e-9+1.000000001*I <- {mu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I}
-1.000000001+.3464101616e-9*I <- {mu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, w[3] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.0, 1.0] <- {Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
-1.0 <- {Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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
Failed [300 / 300]
300/300]: [[-.9062441475+.1226650086*I <- {phi = 1/2*3^(1/2)+1/2*I, a[3] = 1/2*3^(1/2)+1/2*I, b[3] = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I, m = 1}
-1.278771435+1.396327873*I <- {phi = 1/2*3^(1/2)+1/2*I, a[3] = 1/2*3^(1/2)+1/2*I, b[3] = 1/2*3^(1/2)+1/2*I, w[3] = 1/2*3^(1/2)+1/2*I, m = 2}
Failed [300 / 300]
{Complex[-0.9062441474191866, 0.12266500824612203] <- {Rule[m, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-1.2787714355239146, 1.3963278722366796] <- {Rule[m, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
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]] Missing Macro Error Failure - Skipped - Because timed out
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 Missing Macro Error Failure - Skipped - Because timed out
30.13.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{1}(\xi_{1}) = w_{1}(\xi_{2})} w[1]*(xi[1]) = w[1]*(xi[2]) Subscript[w, 1]*(Subscript[\[Xi], 1]) == Subscript[w, 1]*(Subscript[\[Xi], 2]) Skipped - no semantic math Skipped - no semantic math - -
30.14#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \xi} 0 < xi 0 < \[Xi] Skipped - no semantic math Skipped - no semantic math - -
30.14#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -1 < \eta} - 1 < eta - 1 < \[Eta] Skipped - no semantic math Skipped - no semantic math - -
30.14#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \phi} 0 <= phi 0 <= \[Phi] Skipped - no semantic math Skipped - no semantic math - -
30.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\xi}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1+\xi^{2}}} (h[xi])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 + (xi)^(2)) (Subscript[h, \[Xi]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 + \[Xi]^(2)] Skipped - no semantic math Skipped - no semantic math - -
30.14.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\eta}^{2} = \frac{c^{2}(\xi^{2}+\eta^{2})}{1-\eta^{2}}} (h[eta])^(2) = ((c)^(2)*((xi)^(2)+ (eta)^(2)))/(1 - (eta)^(2)) (Subscript[h, \[Eta]])^(2) == Divide[(c)^(2)*(\[Xi]^(2)+ \[Eta]^(2)),1 - \[Eta]^(2)] Skipped - no semantic math Skipped - no semantic math - -
30.14.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{\phi}^{2} = c^{2}(\xi^{2}+1)(1-\eta^{2})} (h[phi])^(2) = (c)^(2)*((xi)^(2)+ 1)*(1 - (eta)^(2)) (Subscript[h, \[Phi]])^(2) == (c)^(2)*(\[Xi]^(2)+ 1)*(1 - \[Eta]^(2)) Skipped - no semantic math Skipped - no semantic math - -
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
Failed [260 / 300]
260/300]: [[-.6665112581-1.154431362*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = 1/2*3^(1/2)+1/2*I}
1.154431362-.6665112581*I <- {gamma = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, w[1] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.6666666666666664, -2.309401076758503] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[2.309401076758503, 0.6666666666666662] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
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]] Missing Macro Error Failure - Skipped - Because timed out
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 Missing Macro Error Failure -
Failed [300 / 300]
{Complex[-0.30414296182717676, -0.005578569442222112] <- {Rule[j, 4], Rule[m, 1], Rule[n, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.05539464168732451, -0.030004541724887247] <- {Rule[j, 4], Rule[m, 1], Rule[n, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ξ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
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]}, GenerateConditions->None] == Subscript[\[CapitalLambda], n]*Subscript[\[Phi], n]*(t) Missing Macro Error Missing Macro 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}, GenerateConditions->None] == (- I)^(n)*Sqrt[Divide[2*Pi*\[Tau],\[Sigma]*Subscript[\[CapitalLambda], n]]]*Subscript[\[Phi], n]*(Divide[\[Tau],\[Sigma]]*\[Omega])* Subscript[\[Chi], \[Sigma]]*(\[Omega]) Missing Macro Error Missing Macro 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]}, GenerateConditions->None] == (- I)^(n)*Sqrt[Divide[2*Pi*\[Tau]*Subscript[\[CapitalLambda], n],\[Sigma]]]*Subscript[\[Phi], n]*(Divide[\[Tau],\[Sigma]]*\[Omega]) Missing Macro Error Missing Macro 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]}, GenerateConditions->None] == Subscript[\[CapitalLambda], n]*KroneckerDelta[k, n] Translation Error Translation 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}, GenerateConditions->None] == KroneckerDelta[k, n] Translation Error Translation Error - -
30.15.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{\sqrt{\mathrm{B}}}+\acos@@{\sqrt{\alpha}} = \acos@@{\sqrt{\Lambda_{0}}}} arccos(sqrt(B))+ arccos(sqrt(alpha)) = arccos(sqrt(Lambda[0])) ArcCos[Sqrt[B]]+ ArcCos[Sqrt[\[Alpha]]] == ArcCos[Sqrt[Subscript[\[CapitalLambda], 0]]] Failure Failure
Failed [300 / 300]
300/300]: [[.6584789493*I <- {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = 1/2*3^(1/2)+1/2*I}
-.6623382543+1.000904144*I <- {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[0.0, 0.6584789484624083] <- {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.6623382542357523, 1.0009041434383552] <- {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
30.15.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{B} = \left(\sqrt{\Lambda_{0}\alpha}+\sqrt{1-\Lambda_{0}}\sqrt{1-\alpha}\right)^{2}} B = (sqrt(Lambda[0]*alpha)+sqrt(1 - Lambda[0])*sqrt(1 - alpha))^(2) B == (Sqrt[Subscript[\[CapitalLambda], 0]*\[Alpha]]+Sqrt[1 - Subscript[\[CapitalLambda], 0]]*Sqrt[1 - \[Alpha]])^(2) Skipped - no semantic math Skipped - no semantic math - -
30.15#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \sqrt{\frac{\alpha}{\Lambda_{0}}}} a = sqrt((alpha)/(Lambda[0])) a == Sqrt[Divide[\[Alpha],Subscript[\[CapitalLambda], 0]]] Skipped - no semantic math Skipped - no semantic math - -
30.15#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b = \sqrt{\frac{1-\alpha}{1-\Lambda_{0}}}} b = sqrt((1 - alpha)/(1 - Lambda[0])) b == Sqrt[Divide[1 - \[Alpha],1 - Subscript[\[CapitalLambda], 0]]] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}} A[j , j] = (m + 2*j - 2)*(m + 2*j - 1)- 2*(gamma)^(2)*((m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2))/((2*m + 4*j - 5)*(2*m + 4*j - 1)) Subscript[A, j , j] == (m + 2*j - 2)*(m + 2*j - 1)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2),(2*m + 4*j - 5)*(2*m + 4*j - 1)] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}} A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j - 1)*(2*m + 2*j))/((2*m + 4*j - 1)*(2*m + 4*j + 1)) Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j - 1)*(2*m + 2*j),(2*m + 4*j - 1)*(2*m + 4*j + 1)] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}} A[j , j - 1] = - (gamma)^(2)*((2*j - 3)*(2*j - 2))/((2*m + 4*j - 7)*(2*m + 4*j - 5)) Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 3)*(2*j - 2),(2*m + 4*j - 7)*(2*m + 4*j - 5)] Skipped - no semantic math Skipped - no semantic math - -
30.16.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{j,d+1} \leq \alpha_{j,d}} alpha[j , d + 1] <= alpha[j , d] Subscript[\[Alpha], j , d + 1] <= Subscript[\[Alpha], j , d] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2,2} = 14.18833\;246} alpha[2 , 2] = 14.18833246 Subscript[\[Alpha], 2 , 2] == 14.18833246 Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2,3} = 13.98002\;013} alpha[2 , 3] = 13.98002013 Subscript[\[Alpha], 2 , 3] == 13.98002013 Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2,4} = 13.97907\;459} alpha[2 , 4] = 13.97907459 Subscript[\[Alpha], 2 , 4] == 13.97907459 Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2,5} = 13.97907\;345} alpha[2 , 5] = 13.97907345 Subscript[\[Alpha], 2 , 5] == 13.97907345 Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{2,6} = 13.97907\;345} alpha[2 , 6] = 13.97907345 Subscript[\[Alpha], 2 , 6] == 13.97907345 Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}} A[j , j] = (m + 2*j - 1)*(m + 2*j)- 2*(gamma)^(2)*((m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2))/((2*m + 4*j - 3)*(2*m + 4*j + 1)) Subscript[A, j , j] == (m + 2*j - 1)*(m + 2*j)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2),(2*m + 4*j - 3)*(2*m + 4*j + 1)] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}} A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j)*(2*m + 2*j + 1))/((2*m + 4*j + 1)*(2*m + 4*j + 3)) Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j)*(2*m + 2*j + 1),(2*m + 4*j + 1)*(2*m + 4*j + 3)] Skipped - no semantic math Skipped - no semantic math - -
30.16#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}} A[j , j - 1] = - (gamma)^(2)*((2*j - 2)*(2*j - 1))/((2*m + 4*j - 5)*(2*m + 4*j - 3)) Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 2)*(2*j - 1),(2*m + 4*j - 5)*(2*m + 4*j - 3)] Skipped - no semantic math Skipped - no semantic math - -
30.16.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}} sum(exp(1)(exp(1)[j , d])^(2)*(factorial(n + m + 2*j - 2*p))/(factorial(n - m + 2*j - 2*p))*(1)/(2*n + 4*j - 4*p + 1), j = 1..d) = (factorial(n + m))/(factorial(n - m))*(1)/(2*n + 1) Sum[E(Subscript[E, j , d])^(2)*Divide[(n + m + 2*j - 2*p)!,(n - m + 2*j - 2*p)!]*Divide[1,2*n + 4*j - 4*p + 1], {j, 1, d}, GenerateConditions->None] == Divide[(n + m)!,(n - m)!]*Divide[1,2*n + 1] Skipped - no semantic math Skipped - no semantic math - -
30.16.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n,k}^{m}(\gamma^{2}) = \lim_{d\to\infty}e_{k+p,d}} (a[n , k])^(m)*((gamma)^(2)) = limit(exp(1)[k + p , d], d = infinity) (Subscript[a, n , k])^(m)*(\[Gamma]^(2)) == Limit[Subscript[E, k + p , d], d -> Infinity, GenerateConditions->None] Skipped - no semantic math Skipped - no semantic math - -
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