Gold 71

Jacobi polynomials

Gold ID

71

Link

https://sigir21.wmflabs.org/wiki/Jacobi_polynomials#math.123.0

Formula

$P_{n}^{(\alpha ,\beta )}(z)={\frac {(\alpha +1)_{n}}{n!}}\,{}_{2}F_{1}\left(-n,1+\alpha +\beta +n;\alpha +1;{\tfrac {1}{2}}(1-z)\right)$

TeX Source

P_n^{(\alpha,\beta)}(z)=\frac{(\alpha+1)_n}{n!}\,{}_2F_1\left(-n,1+\alpha+\beta+n;\alpha+1;\tfrac{1}{2}(1-z)\right)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\JacobipolyP{\alpha}{\beta}{n}@{z} = \frac{\Pochhammersym{\alpha + 1}{n}}{n!} \genhyperF{2}{1}@{- n , 1 + \alpha + \beta + n}{\alpha + 1}{\tfrac{1}{2}(1 - z)}

Expected (Gold Entry)

\JacobipolyP{\alpha}{\beta}{n}@{z} = \frac{\Pochhammersym{\alpha + 1}{n}}{n!} \genhyperF{2}{1}@{- n , 1 + \alpha + \beta + n}{\alpha + 1}{\tfrac{1}{2}(1 - z)}

Mathematica

Translation

JacobiP[n, \[Alpha], \[Beta], z] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*HypergeometricPFQ[{- n , 1 + \[Alpha]+ \[Beta]+ n}, {\[Alpha]+ 1}, Divide[1,2]*(1 - z)]

Expected (Gold Entry)

JacobiP[n, \[Alpha], \[Beta], z] == Divide[Pochhammer[\[Alpha]+ 1, n],(n)!]*HypergeometricPFQ[{- n , 1 + \[Alpha]+ \[Beta]+ n}, {\[Alpha]+ 1}, Divide[1,2]*(1 - z)]

Maple

Translation

JacobiP(n, alpha, beta, z) = (pochhammer(alpha + 1, n))/(factorial(n))*hypergeom([- n , 1 + alpha + beta + n], [alpha + 1], (1)/(2)*(1 - z))

Expected (Gold Entry)

JacobiP(n, alpha, beta, z) = (pochhammer(alpha + 1, n))/(factorial(n))*hypergeom([- n , 1 + alpha + beta + n], [alpha + 1], (1)/(2)*(1 - z))