\[\int_{0}^{\infty}e^{-zt}t^{b-1}{\mathbf{M}}\left(a,c,kt\right)\,\mathrm{d}t=%
\Gamma\left(b\right)z^{-b}{{}_{2}{\mathbf{F}}_{1}}\left(a,b;c;\ifrac{k}{z}%
\right),\]