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