:21

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

Bibliography

Equation in Section of KLS.

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