\[\int_{0}^{\infty}e^{-zt}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\,\mathrm{d}t=%
\frac{\Gamma\left(\mu+\nu+\tfrac{1}{2}\right)}{\left(z+\frac{1}{2}\right)^{\mu%
+\nu+\frac{1}{2}}}\*{{}_{2}F_{1}}\left({\tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}+%
\mu+\nu\atop 1+2\mu};\frac{1}{z+\frac{1}{2}}\right),\]