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