\[{\mathbf{M}}\left(a,b,z\right)\sim\frac{e^{z}z^{a-b}}{\Gamma\left(a\right)}%
\sum_{s=0}^{\infty}\frac{{\left(1-a\right)_{s}}{\left(b-a\right)_{s}}}{s!}z^{-%
s}+\frac{e^{\pm\pi\mathrm{i}a}z^{-a}}{\Gamma\left(b-a\right)}\sum_{s=0}^{%
\infty}\frac{{\left(a\right)_{s}}{\left(a-b+1\right)_{s}}}{s!}(-z)^{-s},\]