\[W_{\kappa,\pm\frac{1}{2}n}\left(z\right)=(-1)^{\kappa-\frac{1}{2}n-\frac{1}{2}%
}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}\sum_{k=0}^{\kappa-\frac{1}{2}n-%
\frac{1}{2}}\genfrac{(}{)}{0.0pt}{}{\kappa-\frac{1}{2}n-\frac{1}{2}}{k}{\left(%
n+1+k\right)_{\kappa-k-\frac{1}{2}n-\frac{1}{2}}}(-z)^{k},\]