\[\mathsf{P}_{n}\left(\cos\theta_{1}\cos\theta_{2}+\sin\theta_{1}\sin\theta_{2}%
\cos\phi\right)=\sum_{m=-n}^{n}(-1)^{m}\mathsf{P}^{-m}_{n}\left(\cos\theta_{1}%
\right)\mathsf{P}^{m}_{n}\left(\cos\theta_{2}\right)\cos\left(m\phi\right).\]