\[\frac{\Gamma\left(n+\alpha+\beta-\mu+1\right)}{x^{n+\alpha+\beta-\mu+1}}P^{(%
\alpha,\beta-\mu)}_{n}\left(1-2x^{-1}\right)=\int_{x}^{\infty}\frac{\Gamma%
\left(n+\alpha+\beta+1\right)}{y^{n+\alpha+\beta+1}}P^{(\alpha,\beta)}_{n}%
\left(1-2y^{-1}\right)\*\frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\,\mathrm{%
d}y,\]