DLMF:15.9.E1 (Q5091)

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DLMF:15.9.E1
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    P n ( α , β ) ⁡ ( x ) = ( α + 1 ) n n ! ⁢ F ⁡ ( - n , n + α + β + 1 α + 1 ; 1 - x 2 ) . Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Pochhammer 𝛼 1 𝑛 𝑛 Gauss-hypergeometric-F 𝑛 𝑛 𝛼 𝛽 1 𝛼 1 1 𝑥 2 {\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x\right)=\frac{{\left% (\alpha+1\right)_{n}}}{n!}F\left({-n,n+\alpha+\beta+1\atop\alpha+1};\frac{1-x}% {2}\right).}}
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    DLMF:15.9.E1
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