\[\mathsf{P}^{m}_{\nu}\left(x\right)=(-1)^{m}\frac{\Gamma\left(\nu+m+1\right)}{%
\Gamma\left(\nu-m+1\right)}\left(\frac{1-x}{1+x}\right)^{m/2}\mathbf{F}\left(%
\nu+1,-\nu;m+1;\tfrac{1}{2}-\tfrac{1}{2}x\right).\]