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