\[M_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{\frac{1}{2}+\mu}\sum_{s=0}^{%
\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(1+2\mu\right)_{%
s}}s!}z^{s}=z^{\frac{1}{2}+\mu}\sum_{n=0}^{\infty}{{}_{2}F_{1}}\left({-n,%
\tfrac{1}{2}+\mu-\kappa\atop 1+2\mu};2\right)\frac{\left(-\tfrac{1}{2}z\right)%
^{n}}{n!},\]