\[P^{m}_{\nu}\left(x\right)=\frac{{\left(\nu+1\right)_{m}}}{\pi}\*\int_{0}^{\pi}%
\left(x+\left(x^{2}-1\right)^{1/2}\cos\phi\right)^{\nu}\cos\left(m\phi\right)%
\,\mathrm{d}\phi,\]