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