\[M\left(a,b,z\right)={\mathrm{e}}^{\nu z}\frac{\Gamma^{*}(b)}{\Gamma^{*}(a)}%
\left(1+\frac{(1-\nu)(1+6\nu^{2}z^{2})}{12a}+O\left(\frac{1}{\min(a^{2},b^{2})%
}\right)\right),\]