\[M_{\kappa,\mu}\left(z\right)\sim\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(%
\frac{1}{2}+\mu-\kappa\right)}e^{\frac{1}{2}z}z^{-\kappa}\*\sum_{s=0}^{\infty}%
\frac{{\left(\frac{1}{2}-\mu+\kappa\right)_{s}}{\left(\frac{1}{2}+\mu+\kappa%
\right)_{s}}}{s!}z^{-s}+\frac{\Gamma\left(1+2\mu\right)}{\Gamma\left(\frac{1}{%
2}+\mu+\kappa\right)}e^{-\frac{1}{2}z\pm(\frac{1}{2}+\mu-\kappa)\pi\mathrm{i}}%
z^{\kappa}\*\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}%
{\left(\frac{1}{2}-\mu-\kappa\right)_{s}}}{s!}(-z)^{-s},\]