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