\[P_{n}\left(\cos\theta\right)=\frac{2^{\frac{1}{2}}}{\pi}\int_{0}^{\theta}\frac%
{\cos\left((n+\tfrac{1}{2})\phi\right)}{(\cos\phi-\cos\theta)^{\frac{1}{2}}}\,%
\mathrm{d}\phi,\]