Formula:6447

Digital Library of Mathematical Functions ID 18.17.E9

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

Constraint(s)

${\displaystyle{\displaystyle-1<x<1}}$

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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