\[Y_{{l},{m}}\left(\theta,\phi\right)=\frac{(-1)^{l+m}}{2^{l}l!}\left(\frac{(l-m%
)!(2l+1)}{4\pi(l+m)!}\right)^{1/2}e^{im\phi}\left(\sin\theta\right)^{m}\*\left%
(\frac{\mathrm{d}}{\mathrm{d}(\cos\theta)}\right)^{l+m}\left(\sin\theta\right)%
^{2l}.\]