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