\[W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2}z}}{2\pi\mathrm{i}}\*\int_{-%
\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(\frac{1}{2}+\mu+t\right)%
\Gamma\left(\frac{1}{2}-\mu+t\right)\Gamma\left(-\kappa-t\right)}{\Gamma\left(%
\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}z^{-t}%
\,\mathrm{d}t,\]