Formula:6502

Digital Library of Mathematical Functions ID 18.18.E15

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

Symbols List

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

Resources that cite this formula

No records found.