P n − 1 2 m ( cosh ξ ) = Γ ( n + m + 1 2 ) Γ ( n − m + 1 2 ) ( 2 π sinh ξ ) 1 / 2 Q m − 1 2 n ( coth ξ ) 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)