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