\[\lim_{2\mu\to-n-1}\frac{M_{\kappa,\mu}\left(z\right)}{\Gamma\left(2\mu+1\right%
)}=\frac{{\left(-\frac{1}{2}n-\kappa\right)_{n+1}}}{(n+1)!}M_{\kappa,\frac{1}{%
2}(n+1)}\left(z\right)=e^{-\frac{1}{2}z}z^{-\frac{1}{2}n}\sum_{s=n+1}^{\infty}%
\frac{{\left(-\frac{1}{2}n-\kappa\right)_{s}}}{\Gamma\left(s-n\right)s!}z^{s}.\]