\[\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\nu-1}%
M_{\kappa,\mu}\left(t\right)\,\mathrm{d}t=\frac{\Gamma\left(\mu+\nu+\frac{1}{2%
}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa%
\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)},\]