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