\[e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\kappa}\sum_{n=0}^{\infty}\frac{{%
\left(\frac{1}{2}+\mu-\kappa\right)_{n}}y^{n}}{n!(x+y)^{n}}M_{\kappa-n,\mu}%
\left(x\right),\]