\[\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=\frac{2^{1/2}(\sin\theta)^{\mu}}%
{\pi^{1/2}\Gamma\left(\frac{1}{2}-\mu\right)}\int_{0}^{\theta}\frac{\cos\left(%
\left(\nu+\frac{1}{2}\right)t\right)}{(\cos t-\cos\theta)^{\mu+(1/2)}}\,%
\mathrm{d}t,\]