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