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