Formula:6501

Digital Library of Mathematical Functions ID 18.18.E14

${\displaystyle{\displaystyle P^{(\gamma,\beta)}_{n}\left(x\right)=\dfrac{{\left(\beta+1\right)_{n}}}{{\left(\alpha+\beta+2\right)_{n}}}\sum_{\ell=0}^{n}\dfrac{\alpha+\beta+2\ell+1}{\alpha+\beta+1}\dfrac{{\left(\alpha+\beta+1\right)_{\ell}}{\left(n+\beta+\gamma+1\right)_{\ell}}}{{\left(\beta+1\right)_{\ell}}{\left(n+\alpha+\beta+2\right)_{\ell}}}\dfrac{{\left(\gamma-\alpha\right)_{n-\ell}}}{(n-\ell)!}P^{(\alpha,\beta)}_{\ell}\left(x\right),}}$

Symbols List

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

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