\[\left(1-x^{2}\right)\frac{\mathrm{d}\mathsf{P}^{\mu}_{\nu}\left(x\right)}{%
\mathrm{d}x}=(\nu+\mu)\mathsf{P}^{\mu}_{\nu-1}\left(x\right)-\nu x\mathsf{P}^{%
\mu}_{\nu}\left(x\right).\]