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