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