Formula:6488

Digital Library of Mathematical Functions ID 18.18.E1

${\displaystyle{\displaystyle a_{n}=\frac{n!(2n+\alpha+\beta+1)\Gamma\left(n+\alpha+\beta+1\right)}{2^{\alpha+\beta+1}\Gamma\left(n+\alpha+1\right)\Gamma\left(n+\beta+1\right)}\*\int_{-1}^{1}f(x)P^{(\alpha,\beta)}_{n}\left(x\right)(1-x)^{\alpha}(1+x)^{\beta}\mathrm{d}x.}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle f(z)}}$: analytic function
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.