Results of Lamé Functions

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Revision as of 06:29, 16 October 2020 by Admin (talk | contribs) (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
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DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
29.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k})w = 0} diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2))* w = 0 D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2))* w == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.9359870183-.3879581426*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 1}
-.5826053060-2.538844794*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 2}
Failed [300 / 300]
{Complex[0.9359870178672973, -0.3879581414973573] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5826053037338313, -2.538844793552361] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.2.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{\xi}+\frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)\deriv{w}{\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi-k^{-2})}w = 0} diff(w, [xi$(2)])+(1)/(2)*((1)/(xi)+(1)/(xi - 1)+(1)/(xi - (k)^(- 2)))* diff(w, xi)+(h*(k)^(- 2)- nu*(nu + 1)* xi)/(4*xi*(xi - 1)*(xi - (k)^(- 2)))*w = 0 D[w, {\[Xi], 2}]+Divide[1,2]*(Divide[1,\[Xi]]+Divide[1,\[Xi]- 1]+Divide[1,\[Xi]- (k)^(- 2)])* D[w, \[Xi]]+Divide[h*(k)^(- 2)- \[Nu]*(\[Nu]+ 1)* \[Xi],4*\[Xi]*(\[Xi]- 1)*(\[Xi]- (k)^(- 2))]*w == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.9804044245+.4985385652*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 1}
.3643094905+3.048781532*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 2}
Failed [300 / 300]
{Complex[0.9804044230224559, 0.49853856488927895] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.36430949083593944, 3.048781532678858] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.2.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-k^{2}\cos^{2}@@{\phi})\deriv[2]{w}{\phi}+k^{2}\cos@@{\phi}\sin@@{\phi}\deriv{w}{\phi}+(h-\nu(\nu+1)k^{2}\cos^{2}@@{\phi})w = 0} (1 - (k)^(2)* (cos(phi))^(2))* diff(w, [phi$(2)])+ (k)^(2)* cos(phi)*sin(phi)*diff(w, phi)+(h - nu*(nu + 1)*(k)^(2)* (cos(phi))^(2))* w = 0 (1 - (k)^(2)* (Cos[\[Phi]])^(2))* D[w, {\[Phi], 2}]+ (k)^(2)* Cos[\[Phi]]*Sin[\[Phi]]*D[w, \[Phi]]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (Cos[\[Phi]])^(2))* w == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.9359870183-.3879581426*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 1}
-.5826053060-2.538844794*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 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, k = 2}
Failed [300 / 300]
{Complex[0.09035331946182407, -0.66279682113597] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[z, Rational[3, 2]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.4348106213983929, 0.6227353307293972] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[z, Rational[3, 2]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e_{1}+e_{2}+e_{3} = 0} e[1]+ e[2]+ e[3] = 0 Subscript[e, 1]+ Subscript[e, 2]+ Subscript[e, 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.2#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ifrac{(e_{2}-e_{3})}{(e_{1}-e_{3})} = k^{2}} (e[2]- e[3])/(e[1]- e[3]) = (k)^(2) Divide[Subscript[e, 2]- Subscript[e, 3],Subscript[e, 1]- Subscript[e, 3]] == (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\deriv[2]{w}{\zeta}+\frac{1}{2}\left(\frac{1}{\zeta-e_{1}}+\frac{1}{\zeta-e_{2}}+\frac{1}{\zeta-e_{3}}\right)\deriv{w}{\zeta}}+\frac{g-\nu(\nu+1)\zeta}{4(\zeta-e_{1})(\zeta-e_{2})(\zeta-e_{3})}w = 0} diff(w, [zeta$(2)])+(1)/(2)*((1)/(zeta - e[1])+(1)/(zeta - e[2])+(1)/(zeta - e[3]))* diff(w, zeta)+(g - nu*(nu + 1)* zeta)/(4*(zeta - e[1])*(zeta - e[2])*(zeta - e[3]))*w = 0 D[w, {\[Zeta], 2}]+Divide[1,2]*(Divide[1,\[Zeta]- Subscript[e, 1]]+Divide[1,\[Zeta]- Subscript[e, 2]]+Divide[1,\[Zeta]- Subscript[e, 3]])* D[w, \[Zeta]]+Divide[g - \[Nu]*(\[Nu]+ 1)* \[Zeta],4*(\[Zeta]- Subscript[e, 1])*(\[Zeta]- Subscript[e, 2])*(\[Zeta]- Subscript[e, 3])]*w == 0 Failure Missing Macro Error Error -
29.3#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-3)(\nu+2p+4)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 3)*(nu + 2*p + 4)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 3)*(\[Nu]+ 2*p + 4)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{p} = (2p+2)^{2}(2-k^{2})} beta[p] = (2*p + 2)^(2)*(2 - (k)^(2)) Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2)) Skipped - no semantic math Skipped - no semantic math - -
29.3#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)A_{0}+\alpha_{0}A_{2} = 0} (beta[0]- H)* A[0]+ alpha[0]*A[2] = 0 (Subscript[\[Beta], 0]- H)* Subscript[A, 0]+ Subscript[\[Alpha], 0]*Subscript[A, 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}A_{2p-2}+(\beta_{p}-H)A_{2p}+\alpha_{p}A_{2p+2} = 0} gamma[p]*A[2*p - 2]+(beta[p]- H)* A[2*p]+ alpha[p]*A[2*p + 2] = 0 Subscript[\[Gamma], p]*Subscript[A, 2*p - 2]+(Subscript[\[Beta], p]- H)* Subscript[A, 2*p]+ Subscript[\[Alpha], p]*Subscript[A, 2*p + 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1} (1)/(2)*(A[0])^(2)sum(A(A[2*p])^(2), p = 1..infinity) = 1 Divide[1,2]*(Subscript[A, 0])^(2)Sum[A(Subscript[A, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0} (1)/(2)*A[0]+ sum(A[2*p], p = 1..infinity) > 0 Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((A[2*p + 2])/(A[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[A, 2*p + 2],Subscript[A, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)C_{0}+\alpha_{0}C_{2} = 0} (beta[0]- H)* C[0]+ alpha[0]*C[2] = 0 (Subscript[\[Beta], 0]- H)* Subscript[C, 0]+ Subscript[\[Alpha], 0]*Subscript[C, 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}C_{2p-2}+(\beta_{p}-H)C_{2p}+\alpha_{p}C_{2p+2} = 0} gamma[p]*C[2*p - 2]+(beta[p]- H)* C[2*p]+ alpha[p]*C[2*p + 2] = 0 Subscript[\[Gamma], p]*Subscript[C, 2*p - 2]+(Subscript[\[Beta], p]- H)* Subscript[C, 2*p]+ Subscript[\[Alpha], p]*Subscript[C, 2*p + 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{p} = 4p^{2}(2-k^{2})} beta[p] = 4*(p)^(2)*(2 - (k)^(2)) Subscript[\[Beta], p] == 4*(p)^(2)*(2 - (k)^(2)) Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1} ((1)/(2)*C(C[0])^(2)+ sum(C(C[2*p])^(2), p = 1..infinity))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..infinity) = 1 (Divide[1,2]*C(Subscript[C, 0])^(2)+ Sum[C(Subscript[C, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0} (1)/(2)*C[0]+ sum(C[2*p], p = 1..infinity) > 0 Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((C[2*p + 2])/(C[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[C, 2*p + 2],Subscript[C, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)A_{1}+\alpha_{0}A_{3} = 0} (beta[0]- H)* A[1]+ alpha[0]*A[3] = 0 (Subscript[\[Beta], 0]- H)* Subscript[A, 1]+ Subscript[\[Alpha], 0]*Subscript[A, 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}A_{2p-1}+(\beta_{p}-H)A_{2p+1}+\alpha_{p}A_{2p+3} = 0} gamma[p]*A[2*p - 1]+(beta[p]- H)* A[2*p + 1]+ alpha[p]*A[2*p + 3] = 0 Subscript[\[Gamma], p]*Subscript[A, 2*p - 1]+(Subscript[\[Beta], p]- H)* Subscript[A, 2*p + 1]+ Subscript[\[Alpha], p]*Subscript[A, 2*p + 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}A_{2p+1}^{2} = 1} sum(A(A[2*p + 1])^(2), p = 0..infinity) = 1 Sum[A(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}A_{2p+1} > 0} sum(A[2*p + 1], p = 0..infinity) > 0 Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((A[2*p + 1])/(A[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[A, 2*p + 1],Subscript[A, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)C_{1}+\alpha_{0}C_{3} = 0} (beta[0]- H)* C[1]+ alpha[0]*C[3] = 0 (Subscript[\[Beta], 0]- H)* Subscript[C, 1]+ Subscript[\[Alpha], 0]*Subscript[C, 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}C_{2p-1}+(\beta_{p}-H)C_{2p+1}+\alpha_{p}C_{2p+3} = 0} gamma[p]*C[2*p - 1]+(beta[p]- H)* C[2*p + 1]+ alpha[p]*C[2*p + 3] = 0 Subscript[\[Gamma], p]*Subscript[C, 2*p - 1]+(Subscript[\[Beta], p]- H)* Subscript[C, 2*p + 1]+ Subscript[\[Alpha], p]*Subscript[C, 2*p + 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}C_{2p+1} > 0} sum(C[2*p + 1], p = 0..infinity) > 0 Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((C[2*p + 1])/(C[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[C, 2*p + 1],Subscript[C, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)B_{1}+\alpha_{0}B_{3} = 0} (beta[0]- H)* B[1]+ alpha[0]*B[3] = 0 (Subscript[\[Beta], 0]- H)* Subscript[B, 1]+ Subscript[\[Alpha], 0]*Subscript[B, 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}B_{2p-1}+(\beta_{p}-H)B_{2p+1}+\alpha_{p}B_{2p+3} = 0} gamma[p]*B[2*p - 1]+(beta[p]- H)* B[2*p + 1]+ alpha[p]*B[2*p + 3] = 0 Subscript[\[Gamma], p]*Subscript[B, 2*p - 1]+(Subscript[\[Beta], p]- H)* Subscript[B, 2*p + 1]+ Subscript[\[Alpha], p]*Subscript[B, 2*p + 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}B_{2p+1}^{2} = 1} sum(B(B[2*p + 1])^(2), p = 0..infinity) = 1 Sum[B(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0} sum((2*p + 1)* B[2*p + 1], p = 0..infinity) > 0 Sum[(2*p + 1)* Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E37 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((B[2*p + 1])/(B[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[B, 2*p + 1],Subscript[B, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E39 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)D_{1}+\alpha_{0}D_{3} = 0} (beta[0]- H)* D[1]+ alpha[0]*D[3] = 0 (Subscript[\[Beta], 0]- H)* Subscript[D, 1]+ Subscript[\[Alpha], 0]*Subscript[D, 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E40 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}D_{2p-1}+(\beta_{p}-H)D_{2p+1}+\alpha_{p}D_{2p+3} = 0} gamma[p]*D[2*p - 1]+(beta[p]- H)* D[2*p + 1]+ alpha[p]*D[2*p + 3] = 0 Subscript[\[Gamma], p]*Subscript[D, 2*p - 1]+(Subscript[\[Beta], p]- H)* Subscript[D, 2*p + 1]+ Subscript[\[Alpha], p]*Subscript[D, 2*p + 3] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6.E43 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0} sum((2*p + 1)* D[2*p + 1], p = 0..infinity) > 0 Sum[(2*p + 1)* Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E44 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((D[2*p + 1])/(D[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[D, 2*p + 1],Subscript[D, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E48 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)B_{2}+\alpha_{0}B_{4} = 0} (beta[0]- H)* B[2]+ alpha[0]*B[4] = 0 (Subscript[\[Beta], 0]- H)* Subscript[B, 2]+ Subscript[\[Alpha], 0]*Subscript[B, 4] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E49 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}B_{2p}+(\beta_{p}-H)B_{2p+2}+\alpha_{p}B_{2p+4} = 0} gamma[p]*B[2*p]+(beta[p]- H)* B[2*p + 2]+ alpha[p]*B[2*p + 4] = 0 Subscript[\[Gamma], p]*Subscript[B, 2*p]+(Subscript[\[Beta], p]- H)* Subscript[B, 2*p + 2]+ Subscript[\[Alpha], p]*Subscript[B, 2*p + 4] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E50 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=1}^{\infty}B_{2p}^{2} = 1} sum(B(B[2*p])^(2), p = 1..infinity) = 1 Sum[B(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E51 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0} sum((2*p + 2)* B[2*p + 2], p = 0..infinity) > 0 Sum[(2*p + 2)* Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E52 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((B[2*p + 2])/(B[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[B, 2*p + 2],Subscript[B, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.6.E54 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\beta_{0}-H)D_{2}+\alpha_{0}D_{4} = 0} (beta[0]- H)* D[2]+ alpha[0]*D[4] = 0 (Subscript[\[Beta], 0]- H)* Subscript[D, 2]+ Subscript[\[Alpha], 0]*Subscript[D, 4] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E55 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p}D_{2p}+(\beta_{p}-H)D_{2p+2}+\alpha_{p}D_{2p+4} = 0} gamma[p]*D[2*p]+(beta[p]- H)* D[2*p + 2]+ alpha[p]*D[2*p + 4] = 0 Subscript[\[Gamma], p]*Subscript[D, 2*p]+(Subscript[\[Beta], p]- H)* Subscript[D, 2*p + 2]+ Subscript[\[Alpha], p]*Subscript[D, 2*p + 4] == 0 Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}} alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)* (k)^(2) Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{p} = (2p+2)^{2}(2-k^{2})} beta[p] = (2*p + 2)^(2)*(2 - (k)^(2)) Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2)) Skipped - no semantic math Skipped - no semantic math - -
29.6#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}} gamma[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)* (k)^(2) Subscript[\[Gamma], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)* (k)^(2) Skipped - no semantic math Skipped - no semantic math - -
29.6.E57 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1} sum(D(D[2*p])^(2), p = 1..infinity)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..infinity) = 1 Sum[D(Subscript[D, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.6.E58 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0} sum((2*p + 2)* D[2*p + 2], p = 0..infinity) > 0 Sum[(2*p + 2)* Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.6.E59 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}} limit((D[2*p + 2])/(D[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2)) Limit[Divide[Subscript[D, 2*p + 2],Subscript[D, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)] Skipped - no semantic math Skipped - no semantic math - -
29.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{0} = \frac{1}{2^{3}}(1+k^{2})(1+p^{2})} tau[0] = (1)/((2)^(3))*(1 + (k)^(2))*(1 + (p)^(2)) Subscript[\[Tau], 0] == Divide[1,(2)^(3)]*(1 + (k)^(2))*(1 + (p)^(2)) Skipped - no semantic math Skipped - no semantic math - -
29.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{1} = \frac{p}{2^{6}}((1+k^{2})^{2}(p^{2}+3)-4k^{2}(p^{2}+5))} tau[1] = (p)/((2)^(6))*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5)) Subscript[\[Tau], 1] == Divide[p,(2)^(6)]*((1 + (k)^(2))^(2)*((p)^(2)+ 3)- 4*(k)^(2)*((p)^(2)+ 5)) Skipped - no semantic math Skipped - no semantic math - -
29.7.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{2} = \frac{1}{2^{10}}(1+k^{2})(1-k^{2})^{2}(5p^{4}+34p^{2}+9)} tau[2] = (1)/((2)^(10))*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9) Subscript[\[Tau], 2] == Divide[1,(2)^(10)]*(1 + (k)^(2))*(1 - (k)^(2))^(2)*(5*(p)^(4)+ 34*(p)^(2)+ 9) Skipped - no semantic math Skipped - no semantic math - -
29.7.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{3} = \frac{p}{2^{14}}((1+k^{2})^{4}(33p^{4}+410p^{2}+405)-24k^{2}(1+k^{2})^{2}(7p^{4}+90p^{2}+95)+16k^{4}(9p^{4}+130p^{2}+173))} tau[3] = (p)/((2)^(14))*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173)) Subscript[\[Tau], 3] == Divide[p,(2)^(14)]*((1 + (k)^(2))^(4)*(33*(p)^(4)+ 410*(p)^(2)+ 405)- 24*(k)^(2)*(1 + (k)^(2))^(2)*(7*(p)^(4)+ 90*(p)^(2)+ 95)+ 16*(k)^(4)*(9*(p)^(4)+ 130*(p)^(2)+ 173)) Skipped - no semantic math Skipped - no semantic math - -
29.7.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau_{4} = \frac{1}{2^{16}}((1+k^{2})^{5}(63p^{6}+1260p^{4}+2943p^{2}+486)-8k^{2}(1+k^{2})^{3}(49p^{6}+1010p^{4}+2493p^{2}+432)+16k^{4}(1+k^{2})(35p^{6}+760p^{4}+2043p^{2}+378))} tau[4] = (1)/((2)^(16))*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378)) Subscript[\[Tau], 4] == Divide[1,(2)^(16)]*((1 + (k)^(2))^(5)*(63*(p)^(6)+ 1260*(p)^(4)+ 2943*(p)^(2)+ 486)- 8*(k)^(2)*(1 + (k)^(2))^(3)*(49*(p)^(6)+ 1010*(p)^(4)+ 2493*(p)^(2)+ 432)+ 16*(k)^(4)*(1 + (k)^(2))*(35*(p)^(6)+ 760*(p)^(4)+ 2043*(p)^(2)+ 378)) Skipped - no semantic math Skipped - no semantic math - -
29.8.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = k^{2}\Jacobiellsnk@{z}{k}\Jacobiellsnk@{z_{1}}{k}\Jacobiellsnk@{z_{2}}{k}\Jacobiellsnk@{z_{3}}{k}-\frac{k^{2}}{{k^{\prime}}^{2}}\Jacobiellcnk@{z}{k}\Jacobiellcnk@{z_{1}}{k}\Jacobiellcnk@{z_{2}}{k}\Jacobiellcnk@{z_{3}}{k}+\frac{1}{{k^{\prime}}^{2}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}\Jacobielldnk@{z_{2}}{k}\Jacobielldnk@{z_{3}}{k}} x = (k)^(2)* JacobiSN(x + y*I, k)*JacobiSN(x + y*I[1], k)*JacobiSN(x + y*I[2], k)*JacobiSN(x + y*I[3], k)-((k)^(2))/(1 - (k)^(2))*JacobiCN(x + y*I, k)*JacobiCN(x + y*I[1], k)*JacobiCN(x + y*I[2], k)*JacobiCN(x + y*I[3], k)+(1)/(1 - (k)^(2))*JacobiDN(x + y*I, k)*JacobiDN(x + y*I[1], k)*JacobiDN(x + y*I[2], k)*JacobiDN(x + y*I[3], k) x == (k)^(2)* JacobiSN[x + y*I, (k)^2]*JacobiSN[Subscript[x + y*I, 1], (k)^2]*JacobiSN[Subscript[x + y*I, 2], (k)^2]*JacobiSN[Subscript[x + y*I, 3], (k)^2]-Divide[(k)^(2),1 - (k)^(2)]*JacobiCN[x + y*I, (k)^2]*JacobiCN[Subscript[x + y*I, 1], (k)^2]*JacobiCN[Subscript[x + y*I, 2], (k)^2]*JacobiCN[Subscript[x + y*I, 3], (k)^2]+Divide[1,1 - (k)^(2)]*JacobiDN[x + y*I, (k)^2]*JacobiDN[Subscript[x + y*I, 1], (k)^2]*JacobiDN[Subscript[x + y*I, 2], (k)^2]*JacobiDN[Subscript[x + y*I, 3], (k)^2] Failure Aborted Error
Failed [54 / 54]
{Indeterminate <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5]}
Plus[1.5, Times[Complex[1.6461554600232724, 0.45267954815584505], JacobiCN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiCN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiCN[Subscript[Complex[1.5, -1.5], 3], 4.0]], Times[Complex[0.619203045121549, 0.30086290583863873], JacobiDN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiDN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiDN[Subscript[Complex[1.5, -1.5], 3], 4.0]], Times[Complex[-2.0469921952210957, 3.2763330530501245], JacobiSN[Subscript[Complex[1.5, -1.5], 1], 4.0], JacobiSN[Subscript[Complex[1.5, -1.5], 2], 4.0], JacobiSN[Subscript[Complex[1.5, -1.5], 3], 4.0]]] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5]}
29.8.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu w(z_{1})w(z_{2})w(z_{3}) = \int_{-2\compellintKk@@{k}}^{2\compellintKk@@{k}}\FerrersP[]{\nu}@{x}w(z)\diff{z}} mu*w*(x + y*I[1])* w*(x + y*I[2])* w*(x + y*I[3]) = int(LegendreP(nu, x)*w*((x + y*I)), (x + y*I) = - 2*EllipticK(k)..2*EllipticK(k)) \[Mu]*w*(Subscript[x + y*I, 1])* w*(Subscript[x + y*I, 2])* w*(Subscript[x + y*I, 3]) == Integrate[LegendreP[\[Nu], x]*w*((x + y*I)), {(x + y*I), - 2*EllipticK[(k)^2], 2*EllipticK[(k)^2]}, GenerateConditions->None] Error Failure -
Failed [300 / 300]
{Plus[Times[-1.0, NIntegrate[Complex[2.8644916021274596, 0.010098545944192239] <- {Complex[1.5, -1.5], DirectedInfinity[], DirectedInfinity[]}]], Times[Complex[-0.49999999999999994, 0.8660254037844387], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2], Subscript[Complex[1.5, -1.5], 3]]], {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Times[-1.0, NIntegrate[Complex[2.8644916021274596, 0.010098545944192239] <- {Complex[1.5, -1.5], Times[-2, EllipticK[4]], Times[2, EllipticK[4]]}]], Times[Complex[-0.49999999999999994, 0.8660254037844387], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2], Subscript[Complex[1.5, -1.5], 3]]], {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[y, -1.5], Rule[μ, Power[E, Times[Complex[0, Ration
29.8.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \frac{2\sigma\tau}{\Wronskian@{w,w_{2}}}} mu = (2*sigma*tau)/((w)*diff(w[2], w)-diff(w, w)*(w[2])) \[Mu] == Divide[2*\[Sigma]*\[Tau],Wronskian[{w, Subscript[w, 2]}, w]] Failure Failure
Failed [300 / 300]
300/300]: [[2.598076212+1.500000000*I <- {mu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, w[2] = 1/2*3^(1/2)+1/2*I}
1.866025404-1.232050808*I <- {mu = 1/2*3^(1/2)+1/2*I, sigma = 1/2*3^(1/2)+1/2*I, tau = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, w[2] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-1.0000000000000002, -1.7320508075688772], Power[Plus[Complex[-0.8660254037844387, -0.49999999999999994], Times[Complex[0.8660254037844387, 0.49999999999999994], Derivative[1, 0][Subscript][Complex[0.8660254037844387, 0.49999999999999994], 2.0]]], -1]]] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-1.0000000000000002, -1.7320508075688772], Power[Plus[Complex[0.4999999999999998, -0.8660254037844387], Times[Complex[0.8660254037844387, 0.49999999999999994], Derivative[1, 0][Subscript][Complex[0.8660254037844387, 0.49999999999999994], 2.0]]], -1]]] <- {Rule[w, Power[E, Time
29.8#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z+2\compellintKk@@{k}) = \sigma w(z)} w*(z + 2*EllipticK(k)) = sigma*w*(z) w*(z + 2*EllipticK[(k)^2]) == \[Sigma]*w*(z) Failure Failure Error
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.038160455456161, -1.1586967532026022] <- {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.8#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w_{2}(z+2\compellintKk@@{k}) = \tau w(z)+\sigma w_{2}(z)} w[2]*(z + 2*EllipticK(k)) = tau*w*(z)+ sigma*w[2]*(z) Subscript[w, 2]*(z + 2*EllipticK[(k)^2]) == \[Tau]*w*(z)+ \[Sigma]*Subscript[w, 2]*(z) Failure Failure Error
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.038160455456161, -2.1586967532026025] <- {Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[σ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.8.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \frac{1}{k^{\prime}}\Jacobielldnk@{z}{k}\Jacobielldnk@{z_{1}}{k}} y = (1)/(sqrt(1 - (k)^(2)))*JacobiDN(x + y*I, k)*JacobiDN(x + y*I[1], k) y == Divide[1,Sqrt[1 - (k)^(2)]]*JacobiDN[x + y*I, (k)^2]*JacobiDN[Subscript[x + y*I, 1], (k)^2] Failure Aborted Error
Failed [54 / 54]
{DirectedInfinity[] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5]}
Plus[-1.5, Times[Complex[-0.5211098390253335, 1.072491134351887], JacobiDN[Subscript[Complex[1.5, -1.5], 1], 4.0]]] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5]}
29.11.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{z}{k}+k^{2}\omega^{2}\Jacobiellsnk^{4}@{z}{k})w = 0} diff(w, [z$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(z, k))^(2)+ (k)^(2)* (omega)^(2)* (JacobiSN(z, k))^(4))* w = 0 D[w, {z, 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (k)^(2)* \[Omega]^(2)* (JacobiSN[z, (k)^2])^(4))* w == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.4970479804-.2136667430*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 1}
-.5039614158-1.687364305*I <- {h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, omega = 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, k = 2}
Failed [300 / 300]
{Complex[0.4970479802306743, -0.21366674241821534] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5039614145885605, -1.6873643054323533] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.12.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < \xi_{1}} 0 < xi[1] 0 < Subscript[\[Xi], 1] Skipped - no semantic math Skipped - no semantic math - -
29.12.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq t_{1}} 0 <= t[1] 0 <= Subscript[t, 1] Skipped - no semantic math Skipped - no semantic math - -
29.14.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(s,t) = \Jacobiellsnk^{2}@{\compellintKk@@{k}+\iunit t}{k}-\Jacobiellsnk^{2}@{s}{k}} w*(s , t) = (JacobiSN(EllipticK(k)+ I*t, k))^(2)- (JacobiSN(s, k))^(2) w*(s , t) == (JacobiSN[EllipticK[(k)^2]+ I*t, (k)^2])^(2)- (JacobiSN[s, (k)^2])^(2) Failure Failure Error Error
29.15.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H_{0} < H_{1}} H[0] < H[1] Subscript[H, 0] < Subscript[H, 1] Skipped - no semantic math Skipped - no semantic math - -
29.15.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{n}A_{2p}^{2} = 1} (1)/(2)*(A[0])^(2)sum(A(A[2*p])^(2), p = 1..n) = 1 Divide[1,2]*(Subscript[A, 0])^(2)Sum[A(Subscript[A, 2*p])^(2), {p, 1, n}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}A_{0}+\sum_{p=1}^{n}A_{2p} > 0} (1)/(2)*A[0]+ sum(A[2*p], p = 1..n) > 0 Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}A_{2p+1}^{2} = 1} sum(A(A[2*p + 1])^(2), p = 0..n) = 1 Sum[A(Subscript[A, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}A_{2p+1} > 0} sum(A[2*p + 1], p = 0..n) > 0 Sum[Subscript[A, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}B_{2p+1}^{2} = 1} sum(B(B[2*p + 1])^(2), p = 0..n) = 1 Sum[B(Subscript[B, 2*p + 1])^(2), {p, 0, n}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+1)B_{2p+1} > 0} sum((2*p + 1)* B[2*p + 1], p = 0..n) > 0 Sum[(2*p + 1)* Subscript[B, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{n}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{n-1}C_{2p}C_{2p+2} = 1} ((1)/(2)*C(C[0])^(2)+ sum(C(C[2*p])^(2), p = 1..n))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..n - 1) = 1 (Divide[1,2]*C(Subscript[C, 0])^(2)+ Sum[C(Subscript[C, 2*p])^(2), {p, 1, n}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, n - 1}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p} > 0} (1)/(2)*C[0]+ sum(C[2*p], p = 1..n) > 0 Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}B_{2p+2}^{2} = 1} sum(B(B[2*p + 2])^(2), p = 0..n) = 1 Sum[B(Subscript[B, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+2)B_{2p+2} > 0} sum((2*p + 2)* B[2*p + 2], p = 0..n) > 0 Sum[(2*p + 2)* Subscript[B, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}C_{2p+1} > 0} sum(C[2*p + 1], p = 0..n) > 0 Sum[Subscript[C, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E36 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+1)D_{2p+1} > 0} sum((2*p + 1)* D[2*p + 1], p = 0..n) > 0 Sum[(2*p + 1)* Subscript[D, 2*p + 1], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.15.E40 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=0}^{n}D_{2p+2}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{n}D_{2p}D_{2p+2} = 1} sum(D(D[2*p + 2])^(2), p = 0..n)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..n) = 1 Sum[D(Subscript[D, 2*p + 2])^(2), {p, 0, n}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, n}, GenerateConditions->None] == 1 Skipped - no semantic math Skipped - no semantic math - -
29.15.E41 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{p=0}^{n}(2p+2)D_{2p+2} > 0} sum((2*p + 2)* D[2*p + 2], p = 0..n) > 0 Sum[(2*p + 2)* Subscript[D, 2*p + 2], {p, 0, n}, GenerateConditions->None] > 0 Skipped - no semantic math Skipped - no semantic math - -
29.18#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = kr\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}} x = k*r*JacobiSN(beta, k)*JacobiSN(gamma, k) x == k*r*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[2.206882914 <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, x = 3/2, k = 1}
1.742014676 <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, x = 3/2, k = 2}
Failed [300 / 300]
{Complex[2.5758629567327462, 0.3306870492079255] <- {Rule[k, 1], Rule[r, -1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.8681877710203056, -0.008479026933090933] <- {Rule[k, 2], Rule[r, -1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = \iunit\frac{k}{k^{\prime}}r\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}} y = I*(k)/(sqrt(1 - (k)^(2)))*r*JacobiCN(beta, k)*JacobiCN(gamma, k) y == I*Divide[k,Sqrt[1 - (k)^(2)]]*r*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[-1.500000000+Float(infinity)*I <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, y = -3/2, k = 1}
.24058897e-1 <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, y = -3/2, k = 2}
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[r, -1.5], Rule[y, -1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.25004703976217724, 0.0247093927223503] <- {Rule[k, 2], Rule[r, -1.5], Rule[y, -1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{1}{k^{\prime}}r\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}} z = (1)/(sqrt(1 - (k)^(2)))*r*JacobiDN(beta, k)*JacobiDN(gamma, k) z == Divide[1,Sqrt[1 - (k)^(2)]]*r*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[Float(infinity)+.5000000000*I <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, z = 1/2*3^(1/2)+1/2*I, k = 1}
.8660254040+.8623901524*I <- {beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, r = -3/2, z = 1/2*3^(1/2)+1/2*I, k = 2}
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.6104237277084903, 0.46270316084846885] <- {Rule[k, 2], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r \geq 0} r >= 0 r >= 0 Skipped - no semantic math Skipped - no semantic math - -
29.18#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \gamma} 0 <= gamma 0 <= \[Gamma] Failure Failure
Failed [3 / 10]
3/10]: [[0. <= -1.500000000 <- {gamma = -3/2}
0. <= -.5000000000 <- {gamma = -1/2}
Failed [7 / 10]
{LessEqual[0.0, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
LessEqual[0.0, Complex[-0.4999999999999998, 0.8660254037844387]] <- {Rule[γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
29.18#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma \leq 4\compellintKk@@{k}} gamma <= 4*EllipticK(k) \[Gamma] <= 4*EllipticK[(k)^2] Failure Failure Error
Failed [30 / 30]
{LessEqual[Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[]] <- {Rule[k, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
LessEqual[Complex[0.8660254037844387, 0.49999999999999994], Complex[3.3715007096251925, -4.313031294999287]] <- {Rule[k, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(r,\beta,\gamma) = u_{1}(r)u_{2}(\beta)u_{3}(\gamma)} u*(r , beta , gamma) = u[1]*(r)* u[2]*(beta)* u[3]*(gamma) u*(r , \[Beta], \[Gamma]) == Subscript[u, 1]*(r)* Subscript[u, 2]*(\[Beta])* Subscript[u, 3]*(\[Gamma]) Skipped - no semantic math Skipped - no semantic math - -
29.18.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{r}\left(r^{2}\deriv{u_{1}}{r}\right)+(\omega^{2}r^{2}-\nu(\nu+1))u_{1} = 0} diff(((r)^(2)* diff(u[1], r))+((omega)^(2)* (r)^(2)- nu*(nu + 1))* u[1], r) = 0 D[((r)^(2)* D[Subscript[u, 1], r])+(\[Omega]^(2)* (r)^(2)- \[Nu]*(\[Nu]+ 1))* Subscript[u, 1], r] == 0 Failure Failure
Failed [300 / 300]
300/300]: [[-.9701216577e-9-3.000000003*I <- {nu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, r = -3/2, u[1] = 1/2*3^(1/2)+1/2*I}
3.000000003-.1039230485e-8*I <- {nu = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, r = -3/2, u[1] = -1/2+1/2*I*3^(1/2)}
Failed [300 / 300]
{Complex[-4.440892098500626*^-16, -3.0] <- {Rule[r, -1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[3.0, -1.1102230246251565*^-15] <- {Rule[r, -1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
29.18.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u_{2}}{\beta}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\beta}{k})u_{2} = 0} diff(u[2], [beta$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(beta, k))^(2))* u[2] = 0 D[Subscript[u, 2], {\[Beta], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Beta], (k)^2])^(2))* Subscript[u, 2] == 0 Failure Failure
Failed [300 / 300]
300/300]: [[.9035331887e-1-.6627968211*I <- {beta = 3/2, h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, u[2] = 1/2*3^(1/2)+1/2*I, k = 1}
.4348106217+.6227353309*I <- {beta = 3/2, h = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, u[2] = 1/2*3^(1/2)+1/2*I, k = 2}
Failed [300 / 300]
{Complex[0.09035331946182387, -0.6627968211359702] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[β, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.4348106213983929, 0.6227353307293972] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[β, 1.5], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{u_{3}}{\gamma}+(h-\nu(\nu+1)k^{2}\Jacobiellsnk^{2}@{\gamma}{k})u_{3} = 0} diff(u[3], [gamma$(2)])+(h - nu*(nu + 1)*(k)^(2)* (JacobiSN(gamma, k))^(2))* u[3] = 0 D[Subscript[u, 3], {\[Gamma], 2}]+(h - \[Nu]*(\[Nu]+ 1)*(k)^(2)* (JacobiSN[\[Gamma], (k)^2])^(2))* Subscript[u, 3] == 0 Error Failure -
Failed [300 / 300]
{Complex[0.9359870178672973, -0.3879581414973573] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 1], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.5826053037338313, -2.538844793552361] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[k, 2], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[u, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = k\Jacobiellsnk@{\alpha}{k}\Jacobiellsnk@{\beta}{k}\Jacobiellsnk@{\gamma}{k}} x = k*JacobiSN(alpha, k)*JacobiSN(beta, k)*JacobiSN(gamma, k) x == k*JacobiSN[\[Alpha], (k)^2]*JacobiSN[\[Beta], (k)^2]*JacobiSN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[1.073444110 <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}
1.470871115 <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2}
Failed [300 / 300]
{Complex[0.8507896823681017, -0.1995472033956852] <- {Rule[k, 1], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.4556849214429664, 0.0010205356456730495] <- {Rule[k, 2], Rule[x, 1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = -\frac{k}{k^{\prime}}\Jacobiellcnk@{\alpha}{k}\Jacobiellcnk@{\beta}{k}\Jacobiellcnk@{\gamma}{k}} y = -(k)/(sqrt(1 - (k)^(2)))*JacobiCN(alpha, k)*JacobiCN(beta, k)*JacobiCN(gamma, k) y == -Divide[k,Sqrt[1 - (k)^(2)]]*JacobiCN[\[Alpha], (k)^2]*JacobiCN[\[Beta], (k)^2]*JacobiCN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[Float(infinity) <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1}
-1.500000000-.9993433457*I <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 2}
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-1.4837977605404604, -0.8196088589670207] <- {Rule[k, 2], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \frac{\iunit}{kk^{\prime}}\Jacobielldnk@{\alpha}{k}\Jacobielldnk@{\beta}{k}\Jacobielldnk@{\gamma}{k}} z = (I)/(k*sqrt(1 - (k)^(2)))*JacobiDN(alpha, k)*JacobiDN(beta, k)*JacobiDN(gamma, k) z == Divide[I,k*Sqrt[1 - (k)^(2)]]*JacobiDN[\[Alpha], (k)^2]*JacobiDN[\[Beta], (k)^2]*JacobiDN[\[Gamma], (k)^2] Failure Failure
Failed [300 / 300]
300/300]: [[.8660254040-Float(infinity)*I <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 1}
.7533782555+.5000000000*I <- {alpha = 3/2, beta = 3/2, gamma = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, k = 2}
Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.8776189378612058, 0.7313924592922922] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[γ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
29.18.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u(\alpha,\beta,\gamma) = u_{1}(\alpha)u_{2}(\beta)u_{3}(\gamma)} u*(alpha , beta , gamma) = u[1]*(alpha)* u[2]*(beta)* u[3]*(gamma) u*(\[Alpha], \[Beta], \[Gamma]) == Subscript[u, 1]*(\[Alpha])* Subscript[u, 2]*(\[Beta])* Subscript[u, 3]*(\[Gamma]) Skipped - no semantic math Skipped - no semantic math - -
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