\[\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{\sin\left(\nu\pi\right)}{\pi}\sum_%
{n=0}^{\infty}(-1)^{n}\frac{2n+1}{(\nu-n)(\nu+n+1)}\mathsf{P}^{-\mu}_{n}\left(%
x\right),\]