\[\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi\right)=\frac{\Gamma\left(n+%
\frac{1}{2}\right)}{\Gamma\left(n+m+\tfrac{1}{2}\right)\Gamma\left(n-m+\frac{1%
}{2}\right)}\*\int_{0}^{\infty}\frac{\cosh\left(mt\right)}{(\cosh\xi+\cosh t%
\sinh\xi)^{n+(1/2)}}\,\mathrm{d}t,\]