\[P^{m}_{n-\frac{1}{2}}\left(\cosh\xi\right)=\frac{\Gamma\left(n+m+\tfrac{1}{2}%
\right)}{\Gamma\left(n-m+\tfrac{1}{2}\right)}\*\left(\frac{2}{\pi\sinh\xi}%
\right)^{1/2}\boldsymbol{Q}^{n}_{m-\frac{1}{2}}\left(\coth\xi\right),\]