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