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