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