:18

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