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