\[P^{-\mu}_{\nu}\left(x\right)=\frac{\pi\left(x^{2}-1\right)^{\mu/2}}{2^{\mu}}%
\left(\frac{\mathbf{F}\left(\frac{1}{2}\mu-\frac{1}{2}\nu,\frac{1}{2}\nu+\frac%
{1}{2}\mu+\frac{1}{2};\frac{1}{2};x^{2}\right)}{\Gamma\left(\frac{1}{2}\mu-%
\frac{1}{2}\nu+\frac{1}{2}\right)\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+1%
\right)}-\frac{x\mathbf{F}\left(\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2},%
\frac{1}{2}\nu+\frac{1}{2}\mu+1;\frac{3}{2};x^{2}\right)}{\Gamma\left(\frac{1}%
{2}\mu-\frac{1}{2}\nu\right)\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}%
{2}\right)}\right),\]