Formula:6448

Digital Library of Mathematical Functions ID 18.17.E10

${\displaystyle{\displaystyle\frac{x^{\beta+\mu}(x+1)^{n}}{\Gamma\left(\beta+\mu+n+1\right)}P^{(\alpha,\beta+\mu)}_{n}\left(\frac{x-1}{x+1}\right)=\int_{0}^{x}\frac{y^{\beta}(y+1)^{n}}{\Gamma\left(\beta+n+1\right)}P^{(\alpha,\beta)}_{n}\left(\frac{y-1}{y+1}\right)\*\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y,}}$

Constraint(s)

${\displaystyle{\displaystyle x>0}}$

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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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