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