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