\[\int_{0}^{\infty}e^{-t}t^{b-1}{\mathbf{M}}\left(a,c,t\right)\,\mathrm{d}t=%
\frac{\Gamma\left(b\right)\Gamma\left(c-a-b\right)}{\Gamma\left(c-a\right)%
\Gamma\left(c-b\right)},\]