Orthogonal Polynomials - 18.5 Explicit Representations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
18.5.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{n}@{x} = \cos@{n\theta}}
\ChebyshevpolyT{n}@{x} = \cos@{n\theta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(n, x) = cos(n*theta)

ChebyshevT[n, x] == Cos[n*\[Theta]]
Failure Failure
Failed [90 / 90]
Result: .7694569811+.3969495503*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 1}


Result: 3.747751686+1.159954891*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 2}

... skip entries to safe data
Failed [90 / 90]
Result: Complex[0.7694569809427748, 0.3969495502290325]
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[3.747751685467572, 1.1599548913509004]
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
18.5.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{n}@{x} = \ifrac{(\sin@@{(n+1)\theta})}{\sin@@{\theta}}}
\ChebyshevpolyU{n}@{x} = \ifrac{(\sin@@{(n+1)\theta})}{\sin@@{\theta}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(n, x) = (sin((n + 1)*theta))/(sin(theta))

ChebyshevU[n, x] == Divide[Sin[(n + 1)*\[Theta]],Sin[\[Theta]]]
Failure Failure
Failed [90 / 90]
Result: 1.538913962+.7938991006*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 1}


Result: 7.495503373+2.319909783*I
Test Values: {theta = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 2}

... skip entries to safe data
Failed [90 / 90]
Result: Complex[1.5389139618855496, 0.7938991004580651]
Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[7.495503370935143, 2.3199097827018003]
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
18.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[\alpha]{n}@{\frac{1}{x}} = \frac{(-1)^{n}}{n!}x^{n+\alpha+1}e^{\ifrac{1}{x}}\deriv[n]{}{x}\left(x^{-\alpha-1}e^{-\ifrac{1}{x}}\right)}
\LaguerrepolyL[\alpha]{n}@{\frac{1}{x}} = \frac{(-1)^{n}}{n!}x^{n+\alpha+1}e^{\ifrac{1}{x}}\deriv[n]{}{x}\left(x^{-\alpha-1}e^{-\ifrac{1}{x}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(n, alpha, (1)/(x)) = ((- 1)^(n))/(factorial(n))*(x)^(n + alpha + 1)* exp((1)/(x))*diff((x)^(- alpha - 1)* exp(-(1)/(x)), [x$(n)])

LaguerreL[n, \[Alpha], Divide[1,x]] == Divide[(- 1)^(n),(n)!]*(x)^(n + \[Alpha]+ 1)* Exp[Divide[1,x]]*D[(x)^(- \[Alpha]- 1)* Exp[-Divide[1,x]], {x, n}]
Missing Macro Error Failure -
Failed [24 / 27]
Result: Plus[1.8333333333333335, Times[1.9477340410546757, DifferenceRoot[Function[{, }
Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 1], Plus[Times[-1, ], 1], 1.5, []], Times[Plus[-1, Times[-1, ], 1], Plus[, Times[-1, 1], Times[-2, , 1.5], Times[-3, Power[, 2], 1.5], Times[2, 1, 1.5], Times[3, , 1, 1.5], Times[-1, 1.5], Times[2, 1.5, 1.5], Times[2, , 1.5, 1.5]], [Plus[1, ]]], Times[-1, Plus[Times[-1, ], 1, 1.5], Plus[1, , Times[-1, 1], Times[-4, 1.5], Times[-7, , 1.5], Times[-3, Power[, 2], 1.5], Times[4, 1, 1.5], Times[3, , 1, 1.5], Times[2, 1.5, 1.5], Times[, 1.5, 1.5]], [Plus[2, ]]], Times[Plus[2, ], 1.5, Plus[-1, Times[-1, ], 1, 1.5], Plus[Times[-1, ], 1, 1.5], [Plus[3, ]]]], 0], Equal[[-1], 0], Equal[[0], 0], Equal[[1], Times[Power[E, Times[-1, Power[1.5, -1]]], Binomial[Plus[-1, Times[-1, 1.5]], 1]]]}]][2.0]]], {Rule[n, 1], Rule[x, 1.5], Rule[α, 1.5]}


Result: Plus[2.2638888888888893, Times[-1.9477340410546757, DifferenceRoot[Function[{, }
Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], 1.5, []], Times[Plus[-1, Times[-1, ], 2], Plus[, Times[-1, 2], Times[-2, , 1.5], Times[-3, Power[, 2], 1.5], Times[2, 2, 1.5], Times[3, , 2, 1.5], Times[-1, 1.5], Times[2, 1.5, 1.5], Times[2, , 1.5, 1.5]], [Plus[1, ]]], Times[-1, Plus[Times[-1, ], 2, 1.5], Plus[1, , Times[-1, 2], Times[-4, 1.5], Times[-7, , 1.5], Times[-3, Power[, 2], 1.5], Times[4, 2, 1.5], Times[3, , 2, 1.5], Times[2, 1.5, 1.5], Times[, 1.5, 1.5]], [Plus[2, ]]], Times[Plus[2, ], 1.5, Plus[-1, Times[-1, ], 2, 1.5], Plus[Times[-1, ], 2, 1.5], [Plus[3, ]]]], 0], Equal[[-1], 0], Equal[[0], 0], Equal[[1], Times[Power[E, Times[-1, Power[1.5, -1]]], Binomial[Plus[-1, Times[-1, 1.5]], 2]]]}]][3.0]]], {Rule[n, 2], Rule[x, 1.5], Rule[α, 1.5]}

... skip entries to safe data
18.5.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobipolyP{\alpha}{\beta}{n}@{x} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{n+\alpha+\beta+1}{\ell}\Pochhammersym{\alpha+\ell+1}{n-\ell}}{\ell!\;(n-\ell)!}\left(\frac{x-1}{2}\right)^{\ell}}
\JacobipolyP{\alpha}{\beta}{n}@{x} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{n+\alpha+\beta+1}{\ell}\Pochhammersym{\alpha+\ell+1}{n-\ell}}{\ell!\;(n-\ell)!}\left(\frac{x-1}{2}\right)^{\ell}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
JacobiP(n, alpha, beta, x) = sum((pochhammer(n + alpha + beta + 1, ell)*pochhammer(alpha + ell + 1, n - ell))/(factorial(ell)*factorial(n - ell))*((x - 1)/(2))^(ell), ell = 0..n)

JacobiP[n, \[Alpha], \[Beta], x] == Sum[Divide[Pochhammer[n + \[Alpha]+ \[Beta]+ 1, \[ScriptL]]*Pochhammer[\[Alpha]+ \[ScriptL]+ 1, n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*(Divide[x - 1,2])^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]
Successful Successful - Successful [Tested: 81]
18.5.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{\ell=0}^{n}\frac{\Pochhammersym{n+\alpha+\beta+1}{\ell}\Pochhammersym{\alpha+\ell+1}{n-\ell}}{\ell!\;(n-\ell)!}\left(\frac{x-1}{2}\right)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\genhyperF{2}{1}@@{-n,n+\alpha+\beta+1}{\alpha+1}{\frac{1-x}{2}}}
\sum_{\ell=0}^{n}\frac{\Pochhammersym{n+\alpha+\beta+1}{\ell}\Pochhammersym{\alpha+\ell+1}{n-\ell}}{\ell!\;(n-\ell)!}\left(\frac{x-1}{2}\right)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\genhyperF{2}{1}@@{-n,n+\alpha+\beta+1}{\alpha+1}{\frac{1-x}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((pochhammer(n + alpha + beta + 1, ell)*pochhammer(alpha + ell + 1, n - ell))/(factorial(ell)*factorial(n - ell))*((x - 1)/(2))^(ell), ell = 0..n) = (pochhammer(alpha + 1, n))/(factorial(n))*hypergeom([- n , n + alpha + beta + 1], [alpha + 1], (1 - x)/(2))

Sum[Divide[Pochhammer[n + \[Alpha]+ \[Beta]+ 1, \[ScriptL]]*Pochhammer[\[Alpha]+ \[ScriptL]+ 1, n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*(Divide[x - 1,2])^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*HypergeometricPFQ[{- n , n + \[Alpha]+ \[Beta]+ 1}, {\[Alpha]+ 1}, Divide[1 - x,2]]
Successful Successful - Successful [Tested: 81]
18.5.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobipolyP{\alpha}{\beta}{n}@{x} = 2^{-n}\sum_{\ell=0}^{n}\binom{n+\alpha}{\ell}\binom{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+1)^{\ell}}
\JacobipolyP{\alpha}{\beta}{n}@{x} = 2^{-n}\sum_{\ell=0}^{n}\binom{n+\alpha}{\ell}\binom{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+1)^{\ell}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
JacobiP(n, alpha, beta, x) = (2)^(- n)* sum(binomial(n + alpha,ell)*binomial(n + beta,n - ell)*(x - 1)^(n - ell)*(x + 1)^(ell), ell = 0..n)

JacobiP[n, \[Alpha], \[Beta], x] == (2)^(- n)* Sum[Binomial[n + \[Alpha],\[ScriptL]]*Binomial[n + \[Beta],n - \[ScriptL]]*(x - 1)^(n - \[ScriptL])*(x + 1)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]
Failure Failure Successful [Tested: 81] Successful [Tested: 81]
18.5.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2^{-n}\sum_{\ell=0}^{n}\binom{n+\alpha}{\ell}\binom{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+1)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\left(\frac{x+1}{2}\right)^{n}\genhyperF{2}{1}@@{-n,-n-\beta}{\alpha+1}{\frac{x-1}{x+1}}}
2^{-n}\sum_{\ell=0}^{n}\binom{n+\alpha}{\ell}\binom{n+\beta}{n-\ell}(x-1)^{n-\ell}(x+1)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\left(\frac{x+1}{2}\right)^{n}\genhyperF{2}{1}@@{-n,-n-\beta}{\alpha+1}{\frac{x-1}{x+1}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(2)^(- n)* sum(binomial(n + alpha,ell)*binomial(n + beta,n - ell)*(x - 1)^(n - ell)*(x + 1)^(ell), ell = 0..n) = (pochhammer(alpha + 1, n))/(factorial(n))*((x + 1)/(2))^(n)* hypergeom([- n , - n - beta], [alpha + 1], (x - 1)/(x + 1))

(2)^(- n)* Sum[Binomial[n + \[Alpha],\[ScriptL]]*Binomial[n + \[Beta],n - \[ScriptL]]*(x - 1)^(n - \[ScriptL])*(x + 1)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*(Divide[x + 1,2])^(n)* HypergeometricPFQ[{- n , - n - \[Beta]}, {\[Alpha]+ 1}, Divide[x - 1,x + 1]]
Failure Failure Successful [Tested: 81] Successful [Tested: 81]
18.5.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{n!}\genhyperF{2}{1}@@{-n,n+2\lambda}{\lambda+\tfrac{1}{2}}{\frac{1-x}{2}}}
\ultrasphpoly{\lambda}{n}@{x} = \frac{\Pochhammersym{2\lambda}{n}}{n!}\genhyperF{2}{1}@@{-n,n+2\lambda}{\lambda+\tfrac{1}{2}}{\frac{1-x}{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
GegenbauerC(n, lambda, x) = (pochhammer(2*lambda, n))/(factorial(n))*hypergeom([- n , n + 2*lambda], [lambda +(1)/(2)], (1 - x)/(2))

GegenbauerC[n, \[Lambda], x] == Divide[Pochhammer[2*\[Lambda], n],(n)!]*HypergeometricPFQ[{- n , n + 2*\[Lambda]}, {\[Lambda]+Divide[1,2]}, Divide[1 - x,2]]
Successful Successful -
Failed [15 / 90]
Result: 0.375
Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[λ, -1.5]}


Result: 0.4375
Test Values: {Rule[n, 3], Rule[x, 1.5], Rule[λ, -1.5]}

... skip entries to safe data
18.5.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{x} = \sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-2\ell)!}(2x)^{n-2\ell}}
\ultrasphpoly{\lambda}{n}@{x} = \sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-2\ell)!}(2x)^{n-2\ell}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
GegenbauerC(n, lambda, x) = sum(((- 1)^(ell)* pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - 2*ell))*(2*x)^(n - 2*ell), ell = 0..floor(n/2))

GegenbauerC[n, \[Lambda], x] == Sum[Divide[(- 1)^\[ScriptL]* Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - 2*\[ScriptL])!]*(2*x)^(n - 2*\[ScriptL]), {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]
Failure Successful Manual Skip! Successful [Tested: 90]
18.5.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-2\ell)!}(2x)^{n-2\ell} = (2x)^{n}\frac{\Pochhammersym{\lambda}{n}}{n!}\genhyperF{2}{1}@@{-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}}{1-\lambda-n}{\frac{1}{x^{2}}}}
\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-2\ell)!}(2x)^{n-2\ell} = (2x)^{n}\frac{\Pochhammersym{\lambda}{n}}{n!}\genhyperF{2}{1}@@{-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}}{1-\lambda-n}{\frac{1}{x^{2}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum(((- 1)^(ell)* pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - 2*ell))*(2*x)^(n - 2*ell), ell = 0..floor(n/2)) = (2*x)^(n)*(pochhammer(lambda, n))/(factorial(n))*hypergeom([-(1)/(2)*n , -(1)/(2)*n +(1)/(2)], [1 - lambda - n], (1)/((x)^(2)))

Sum[Divide[(- 1)^\[ScriptL]* Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - 2*\[ScriptL])!]*(2*x)^(n - 2*\[ScriptL]), {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (2*x)^(n)*Divide[Pochhammer[\[Lambda], n],(n)!]*HypergeometricPFQ[{-Divide[1,2]*n , -Divide[1,2]*n +Divide[1,2]}, {1 - \[Lambda]- n}, Divide[1,(x)^(2)]]
Failure Failure Manual Skip!
Failed [3 / 90]
Result: Indeterminate
Test Values: {Rule[n, 3], Rule[x, 1.5], Rule[λ, -2]}


Result: Indeterminate
Test Values: {Rule[n, 3], Rule[x, 0.5], Rule[λ, -2]}

... skip entries to safe data
18.5.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ultrasphpoly{\lambda}{n}@{\cos@@{\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-\ell)!}\cos@{(n-2\ell)\theta}}
\ultrasphpoly{\lambda}{n}@{\cos@@{\theta}} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-\ell)!}\cos@{(n-2\ell)\theta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
GegenbauerC(n, lambda, cos(theta)) = sum((pochhammer(lambda, ell)*pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - ell))*cos((n - 2*ell)*theta), ell = 0..n)

GegenbauerC[n, \[Lambda], Cos[\[Theta]]] == Sum[Divide[Pochhammer[\[Lambda], \[ScriptL]]*Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*Cos[(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None]
Failure Failure Error
Failed [30 / 300]
Result: Indeterminate
Test Values: {Rule[n, 1], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]}


Result: Indeterminate
Test Values: {Rule[n, 2], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]}

... skip entries to safe data
18.5.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-\ell)!}\cos@{(n-2\ell)\theta} = e^{\iunit n\theta}\frac{\Pochhammersym{\lambda}{n}}{n!}\genhyperF{2}{1}@@{-n,\lambda}{1-\lambda-n}{e^{-2\iunit\theta}}}
\sum_{\ell=0}^{n}\frac{\Pochhammersym{\lambda}{\ell}\Pochhammersym{\lambda}{n-\ell}}{\ell!\;(n-\ell)!}\cos@{(n-2\ell)\theta} = e^{\iunit n\theta}\frac{\Pochhammersym{\lambda}{n}}{n!}\genhyperF{2}{1}@@{-n,\lambda}{1-\lambda-n}{e^{-2\iunit\theta}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((pochhammer(lambda, ell)*pochhammer(lambda, n - ell))/(factorial(ell)*factorial(n - ell))*cos((n - 2*ell)*theta), ell = 0..n) = exp(I*n*theta)*(pochhammer(lambda, n))/(factorial(n))*hypergeom([- n , lambda], [1 - lambda - n], exp(- 2*I*theta))

Sum[Divide[Pochhammer[\[Lambda], \[ScriptL]]*Pochhammer[\[Lambda], n - \[ScriptL]],(\[ScriptL])!*(n - \[ScriptL])!]*Cos[(n - 2*\[ScriptL])*\[Theta]], {\[ScriptL], 0, n}, GenerateConditions->None] == Exp[I*n*\[Theta]]*Divide[Pochhammer[\[Lambda], n],(n)!]*HypergeometricPFQ[{- n , \[Lambda]}, {1 - \[Lambda]- n}, Exp[- 2*I*\[Theta]]]
Failure Failure Error
Failed [30 / 300]
Result: Indeterminate
Test Values: {Rule[n, 1], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]}


Result: Indeterminate
Test Values: {Rule[n, 2], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, -2]}

... skip entries to safe data
18.5.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[\alpha]{n}@{x} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\alpha+\ell+1}{n-\ell}}{(n-\ell)!\;\ell!}(-x)^{\ell}}
\LaguerrepolyL[\alpha]{n}@{x} = \sum_{\ell=0}^{n}\frac{\Pochhammersym{\alpha+\ell+1}{n-\ell}}{(n-\ell)!\;\ell!}(-x)^{\ell}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(n, alpha, x) = sum((pochhammer(alpha + ell + 1, n - ell))/(factorial(n - ell)*factorial(ell))*(- x)^(ell), ell = 0..n)

LaguerreL[n, \[Alpha], x] == Sum[Divide[Pochhammer[\[Alpha]+ \[ScriptL]+ 1, n - \[ScriptL]],(n - \[ScriptL])!*(\[ScriptL])!]*(- x)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None]
Missing Macro Error Successful - Successful [Tested: 27]
18.5.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{\ell=0}^{n}\frac{\Pochhammersym{\alpha+\ell+1}{n-\ell}}{(n-\ell)!\;\ell!}(-x)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\genhyperF{1}{1}@@{-n}{\alpha+1}{x}}
\sum_{\ell=0}^{n}\frac{\Pochhammersym{\alpha+\ell+1}{n-\ell}}{(n-\ell)!\;\ell!}(-x)^{\ell} = \frac{\Pochhammersym{\alpha+1}{n}}{n!}\genhyperF{1}{1}@@{-n}{\alpha+1}{x}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((pochhammer(alpha + ell + 1, n - ell))/(factorial(n - ell)*factorial(ell))*(- x)^(ell), ell = 0..n) = (pochhammer(alpha + 1, n))/(factorial(n))*hypergeom([- n], [alpha + 1], x)

Sum[Divide[Pochhammer[\[Alpha]+ \[ScriptL]+ 1, n - \[ScriptL]],(n - \[ScriptL])!*(\[ScriptL])!]*(- x)^\[ScriptL], {\[ScriptL], 0, n}, GenerateConditions->None] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*HypergeometricPFQ[{- n}, {\[Alpha]+ 1}, x]
Successful Successful - Successful [Tested: 27]
18.5.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{n}@{x} = n!\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}(2x)^{n-2\ell}}{\ell!\;(n-2\ell)!}}
\HermitepolyH{n}@{x} = n!\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}(2x)^{n-2\ell}}{\ell!\;(n-2\ell)!}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(n, x) = factorial(n)*sum(((- 1)^(ell)*(2*x)^(n - 2*ell))/(factorial(ell)*factorial(n - 2*ell)), ell = 0..floor(n/2))

HermiteH[n, x] == (n)!*Sum[Divide[(- 1)^\[ScriptL]*(2*x)^(n - 2*\[ScriptL]),(\[ScriptL])!*(n - 2*\[ScriptL])!], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None]
Failure Failure Successful [Tested: 9] Successful [Tested: 9]
18.5.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n!\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}(2x)^{n-2\ell}}{\ell!\;(n-2\ell)!} = (2x)^{n}\genhyperF{2}{0}@@{-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}}{-}{-\frac{1}{x^{2}}}}
n!\sum_{\ell=0}^{\floor{n/2}}\frac{(-1)^{\ell}(2x)^{n-2\ell}}{\ell!\;(n-2\ell)!} = (2x)^{n}\genhyperF{2}{0}@@{-\tfrac{1}{2}n,-\tfrac{1}{2}n+\tfrac{1}{2}}{-}{-\frac{1}{x^{2}}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
factorial(n)*sum(((- 1)^(ell)*(2*x)^(n - 2*ell))/(factorial(ell)*factorial(n - 2*ell)), ell = 0..floor(n/2)) = (2*x)^(n)* hypergeom([-(1)/(2)*n , -(1)/(2)*n +(1)/(2)], [-], -(1)/((x)^(2)))

(n)!*Sum[Divide[(- 1)^\[ScriptL]*(2*x)^(n - 2*\[ScriptL]),(\[ScriptL])!*(n - 2*\[ScriptL])!], {\[ScriptL], 0, Floor[n/2]}, GenerateConditions->None] == (2*x)^(n)* HypergeometricPFQ[{-Divide[1,2]*n , -Divide[1,2]*n +Divide[1,2]}, {-}, -Divide[1,(x)^(2)]]
Error Failure Skip - symbolical successful subtest Error
18.5#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{0}@{x} = 1}
\ChebyshevpolyT{0}@{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(0, x) = 1

ChebyshevT[0, x] == 1
Successful Successful - Successful [Tested: 3]
18.5#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{1}@{x} = x}
\ChebyshevpolyT{1}@{x} = x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(1, x) = x

ChebyshevT[1, x] == x
Successful Successful - Successful [Tested: 3]
18.5#Ex3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{2}@{x} = 2x^{2}-1}
\ChebyshevpolyT{2}@{x} = 2x^{2}-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(2, x) = 2*(x)^(2)- 1

ChebyshevT[2, x] == 2*(x)^(2)- 1
Successful Successful - Successful [Tested: 3]
18.5#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{3}@{x} = 4x^{3}-3x}
\ChebyshevpolyT{3}@{x} = 4x^{3}-3x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(3, x) = 4*(x)^(3)- 3*x

ChebyshevT[3, x] == 4*(x)^(3)- 3*x
Successful Successful - Successful [Tested: 3]
18.5#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{4}@{x} = 8x^{4}-8x^{2}+1}
\ChebyshevpolyT{4}@{x} = 8x^{4}-8x^{2}+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(4, x) = 8*(x)^(4)- 8*(x)^(2)+ 1

ChebyshevT[4, x] == 8*(x)^(4)- 8*(x)^(2)+ 1
Successful Successful - Successful [Tested: 3]
18.5#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{5}@{x} = 16x^{5}-20x^{3}+5x}
\ChebyshevpolyT{5}@{x} = 16x^{5}-20x^{3}+5x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(5, x) = 16*(x)^(5)- 20*(x)^(3)+ 5*x

ChebyshevT[5, x] == 16*(x)^(5)- 20*(x)^(3)+ 5*x
Successful Successful - Successful [Tested: 3]
18.5#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyT{6}@{x} = 32x^{6}-48x^{4}+18x^{2}-1}
\ChebyshevpolyT{6}@{x} = 32x^{6}-48x^{4}+18x^{2}-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevT(6, x) = 32*(x)^(6)- 48*(x)^(4)+ 18*(x)^(2)- 1

ChebyshevT[6, x] == 32*(x)^(6)- 48*(x)^(4)+ 18*(x)^(2)- 1
Successful Successful - Successful [Tested: 3]
18.5#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{0}@{x} = 1}
\ChebyshevpolyU{0}@{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(0, x) = 1

ChebyshevU[0, x] == 1
Successful Successful - Successful [Tested: 3]
18.5#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{1}@{x} = 2x}
\ChebyshevpolyU{1}@{x} = 2x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(1, x) = 2*x

ChebyshevU[1, x] == 2*x
Successful Successful - Successful [Tested: 3]
18.5#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{2}@{x} = 4x^{2}-1}
\ChebyshevpolyU{2}@{x} = 4x^{2}-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(2, x) = 4*(x)^(2)- 1

ChebyshevU[2, x] == 4*(x)^(2)- 1
Successful Successful - Successful [Tested: 3]
18.5#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{3}@{x} = 8x^{3}-4x}
\ChebyshevpolyU{3}@{x} = 8x^{3}-4x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(3, x) = 8*(x)^(3)- 4*x

ChebyshevU[3, x] == 8*(x)^(3)- 4*x
Successful Successful - Successful [Tested: 3]
18.5#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{4}@{x} = 16x^{4}-12x^{2}+1}
\ChebyshevpolyU{4}@{x} = 16x^{4}-12x^{2}+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(4, x) = 16*(x)^(4)- 12*(x)^(2)+ 1
 
ChebyshevU[4, x] == 16*(x)^(4)- 12*(x)^(2)+ 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{5}@{x} = 32x^{5}-32x^{3}+6x}
\ChebyshevpolyU{5}@{x} = 32x^{5}-32x^{3}+6x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(5, x) = 32*(x)^(5)- 32*(x)^(3)+ 6*x
 
ChebyshevU[5, x] == 32*(x)^(5)- 32*(x)^(3)+ 6*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ChebyshevpolyU{6}@{x} = 64x^{6}-80x^{4}+24x^{2}-1}
\ChebyshevpolyU{6}@{x} = 64x^{6}-80x^{4}+24x^{2}-1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
ChebyshevU(6, x) = 64*(x)^(6)- 80*(x)^(4)+ 24*(x)^(2)- 1
 
ChebyshevU[6, x] == 64*(x)^(6)- 80*(x)^(4)+ 24*(x)^(2)- 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{0}@{x} = 1}
\LegendrepolyP{0}@{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(0, x) = 1
 
LegendreP[0, x] == 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{1}@{x} = x}
\LegendrepolyP{1}@{x} = x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(1, x) = x
 
LegendreP[1, x] == x
 Successful Successful - Successful [Tested: 3]
18.5#Ex17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{2}@{x} = \tfrac{3}{2}x^{2}-\tfrac{1}{2}}
\LegendrepolyP{2}@{x} = \tfrac{3}{2}x^{2}-\tfrac{1}{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(2, x) = (3)/(2)*(x)^(2)-(1)/(2)
 
LegendreP[2, x] == Divide[3,2]*(x)^(2)-Divide[1,2]
 Successful Successful - Successful [Tested: 3]
18.5#Ex18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{3}@{x} = \tfrac{5}{2}x^{3}-\tfrac{3}{2}x}
\LegendrepolyP{3}@{x} = \tfrac{5}{2}x^{3}-\tfrac{3}{2}x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(3, x) = (5)/(2)*(x)^(3)-(3)/(2)*x
 
LegendreP[3, x] == Divide[5,2]*(x)^(3)-Divide[3,2]*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{4}@{x} = \tfrac{35}{8}x^{4}-\tfrac{15}{4}x^{2}+\tfrac{3}{8}}
\LegendrepolyP{4}@{x} = \tfrac{35}{8}x^{4}-\tfrac{15}{4}x^{2}+\tfrac{3}{8}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(4, x) = (35)/(8)*(x)^(4)-(15)/(4)*(x)^(2)+(3)/(8)
 
LegendreP[4, x] == Divide[35,8]*(x)^(4)-Divide[15,4]*(x)^(2)+Divide[3,8]
 Successful Successful - Successful [Tested: 3]
18.5#Ex20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{5}@{x} = \tfrac{63}{8}x^{5}-\tfrac{35}{4}x^{3}+\tfrac{15}{8}x}
\LegendrepolyP{5}@{x} = \tfrac{63}{8}x^{5}-\tfrac{35}{4}x^{3}+\tfrac{15}{8}x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(5, x) = (63)/(8)*(x)^(5)-(35)/(4)*(x)^(3)+(15)/(8)*x
 
LegendreP[5, x] == Divide[63,8]*(x)^(5)-Divide[35,4]*(x)^(3)+Divide[15,8]*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LegendrepolyP{6}@{x} = \tfrac{231}{16}x^{6}-\tfrac{315}{16}x^{4}+\tfrac{105}{16}x^{2}-\tfrac{5}{16}}
\LegendrepolyP{6}@{x} = \tfrac{231}{16}x^{6}-\tfrac{315}{16}x^{4}+\tfrac{105}{16}x^{2}-\tfrac{5}{16}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LegendreP(6, x) = (231)/(16)*(x)^(6)-(315)/(16)*(x)^(4)+(105)/(16)*(x)^(2)-(5)/(16)
 
LegendreP[6, x] == Divide[231,16]*(x)^(6)-Divide[315,16]*(x)^(4)+Divide[105,16]*(x)^(2)-Divide[5,16]
 Successful Successful - Successful [Tested: 3]
18.5#Ex22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{0}@{x} = 1}
\LaguerrepolyL[]{0}@{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(0, x) = 1
 
LaguerreL[0, x] == 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{1}@{x} = -x+1}
\LaguerrepolyL[]{1}@{x} = -x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(1, x) = - x + 1
 
LaguerreL[1, x] == - x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{2}@{x} = \tfrac{1}{2}x^{2}-2x+1}
\LaguerrepolyL[]{2}@{x} = \tfrac{1}{2}x^{2}-2x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(2, x) = (1)/(2)*(x)^(2)- 2*x + 1
 
LaguerreL[2, x] == Divide[1,2]*(x)^(2)- 2*x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{3}@{x} = -\tfrac{1}{6}x^{3}+\tfrac{3}{2}x^{2}-3x+1}
\LaguerrepolyL[]{3}@{x} = -\tfrac{1}{6}x^{3}+\tfrac{3}{2}x^{2}-3x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(3, x) = -(1)/(6)*(x)^(3)+(3)/(2)*(x)^(2)- 3*x + 1
 
LaguerreL[3, x] == -Divide[1,6]*(x)^(3)+Divide[3,2]*(x)^(2)- 3*x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{4}@{x} = \tfrac{1}{24}x^{4}-\tfrac{2}{3}x^{3}+3x^{2}-4x+1}
\LaguerrepolyL[]{4}@{x} = \tfrac{1}{24}x^{4}-\tfrac{2}{3}x^{3}+3x^{2}-4x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(4, x) = (1)/(24)*(x)^(4)-(2)/(3)*(x)^(3)+ 3*(x)^(2)- 4*x + 1
 
LaguerreL[4, x] == Divide[1,24]*(x)^(4)-Divide[2,3]*(x)^(3)+ 3*(x)^(2)- 4*x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{5}@{x} = -\tfrac{1}{120}x^{5}+\tfrac{5}{24}x^{4}-\tfrac{5}{3}x^{3}+5x^{2}-5x+1}
\LaguerrepolyL[]{5}@{x} = -\tfrac{1}{120}x^{5}+\tfrac{5}{24}x^{4}-\tfrac{5}{3}x^{3}+5x^{2}-5x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(5, x) = -(1)/(120)*(x)^(5)+(5)/(24)*(x)^(4)-(5)/(3)*(x)^(3)+ 5*(x)^(2)- 5*x + 1
 
LaguerreL[5, x] == -Divide[1,120]*(x)^(5)+Divide[5,24]*(x)^(4)-Divide[5,3]*(x)^(3)+ 5*(x)^(2)- 5*x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[]{6}@{x} = \tfrac{1}{720}x^{6}-\tfrac{1}{20}x^{5}+\tfrac{5}{8}x^{4}-\tfrac{10}{3}x^{3}+\tfrac{15}{2}x^{2}-6x+1}
\LaguerrepolyL[]{6}@{x} = \tfrac{1}{720}x^{6}-\tfrac{1}{20}x^{5}+\tfrac{5}{8}x^{4}-\tfrac{10}{3}x^{3}+\tfrac{15}{2}x^{2}-6x+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
LaguerreL(6, x) = (1)/(720)*(x)^(6)-(1)/(20)*(x)^(5)+(5)/(8)*(x)^(4)-(10)/(3)*(x)^(3)+(15)/(2)*(x)^(2)- 6*x + 1
 
LaguerreL[6, x] == Divide[1,720]*(x)^(6)-Divide[1,20]*(x)^(5)+Divide[5,8]*(x)^(4)-Divide[10,3]*(x)^(3)+Divide[15,2]*(x)^(2)- 6*x + 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex29 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{0}@{x} = 1}
\HermitepolyH{0}@{x} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(0, x) = 1
 
HermiteH[0, x] == 1
 Successful Successful - Successful [Tested: 3]
18.5#Ex30 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{1}@{x} = 2x}
\HermitepolyH{1}@{x} = 2x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(1, x) = 2*x
 
HermiteH[1, x] == 2*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{2}@{x} = 4x^{2}-2}
\HermitepolyH{2}@{x} = 4x^{2}-2		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(2, x) = 4*(x)^(2)- 2
 
HermiteH[2, x] == 4*(x)^(2)- 2
 Successful Successful - Successful [Tested: 3]
18.5#Ex32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{3}@{x} = 8x^{3}-12x}
\HermitepolyH{3}@{x} = 8x^{3}-12x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(3, x) = 8*(x)^(3)- 12*x
 
HermiteH[3, x] == 8*(x)^(3)- 12*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{4}@{x} = 16x^{4}-48x^{2}+12}
\HermitepolyH{4}@{x} = 16x^{4}-48x^{2}+12		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(4, x) = 16*(x)^(4)- 48*(x)^(2)+ 12
 
HermiteH[4, x] == 16*(x)^(4)- 48*(x)^(2)+ 12
 Successful Successful - Successful [Tested: 3]
18.5#Ex34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{5}@{x} = 32x^{5}-160x^{3}+120x}
\HermitepolyH{5}@{x} = 32x^{5}-160x^{3}+120x		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(5, x) = 32*(x)^(5)- 160*(x)^(3)+ 120*x
 
HermiteH[5, x] == 32*(x)^(5)- 160*(x)^(3)+ 120*x
 Successful Successful - Successful [Tested: 3]
18.5#Ex35 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HermitepolyH{6}@{x} = 64x^{6}-480x^{4}+720x^{2}-120}
\HermitepolyH{6}@{x} = 64x^{6}-480x^{4}+720x^{2}-120		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
HermiteH(6, x) = 64*(x)^(6)- 480*(x)^(4)+ 720*(x)^(2)- 120
 
HermiteH[6, x] == 64*(x)^(6)- 480*(x)^(4)+ 720*(x)^(2)- 120
 Successful Successful - Successful [Tested: 3]
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