\[{\mathbf{M}}\left(a,b,z\right)=\frac{\Gamma\left(1+a-b\right)}{2\pi\mathrm{i}%
\Gamma\left(a\right)}\int_{0}^{(1+)}e^{zt}t^{a-1}{(t-1)^{b-a-1}}\,\mathrm{d}t,\]