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