\[\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=\frac{2^{\mu+1}(\sin\theta)^{\mu%
}}{\pi^{1/2}}\*\sum_{k=0}^{\infty}\frac{\Gamma\left(\nu+\mu+k+1\right)}{\Gamma%
\left(\nu+k+\frac{3}{2}\right)}\frac{{\left(\mu+\frac{1}{2}\right)_{k}}}{k!}\*%
\sin\left((\nu+\mu+2k+1)\theta\right),\]