\[\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{\sqrt{z}%
e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{0}^{%
\infty}e^{-t}t^{-\kappa-\frac{1}{2}}I_{2\mu}\left(2\sqrt{zt}\right)\,\mathrm{d%
}t,\]