\[P^{-\mu}_{\nu}\left(x\right)=\frac{2^{1/2}\Gamma\left(\mu+\frac{1}{2}\right)%
\left(x^{2}-1\right)^{\mu/2}}{\pi^{1/2}\Gamma\left(\nu+\mu+1\right)\Gamma\left%
(\mu-\nu\right)}\*\int_{0}^{\infty}\frac{\cosh\left(\left(\nu+\frac{1}{2}%
\right)t\right)}{(x+\cosh t)^{\mu+(1/2)}}\,\mathrm{d}t,\]