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