Formula:6512

Digital Library of Mathematical Functions ID 18.18.E25

${\displaystyle{\displaystyle\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}\frac{P^{(\alpha,\beta)}_{n}\left(y\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}=\sum_{\ell=0}^{n}b_{n,\ell}(x+y)^{\ell}\*\frac{P^{(\alpha,\beta)}_{\ell}\left(\ifrac{(1+xy)}{(x+y)}\right)}{P^{(\alpha,\beta)}_{\ell}\left(1\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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