:09

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P n ( α , β ) ⁡ ( 1 ) = ( α + 1 ) n n ! ⁢ P n ( α , β ) ⁡ ( - 1 ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 Pochhammer-symbol 𝛼 1 𝑛 𝑛 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(1\right% )=\frac{{\left(\alpha+1\right)_{n}}}{n!}P^{(\alpha,\beta)}_{n}\left(-1\right)}}}

Proof

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Symbols List

P n ( α , β ) subscript superscript 𝑃 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section of KLS.

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