\[\int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}W_{\kappa,\mu}%
\left(t\right)J_{\nu}\left(2\sqrt{xt}\right)\,\mathrm{d}t=\frac{\Gamma\left(%
\nu-2\mu+1\right)}{\Gamma\left(\frac{3}{2}-\mu-\kappa+\nu\right)}\*e^{-\frac{1%
}{2}x}x^{\frac{1}{2}(\mu+\kappa-\frac{3}{2})}\*M_{\frac{1}{2}(\kappa-3\mu+\nu+%
\frac{1}{2}),\frac{1}{2}(\nu-\mu-\kappa+\frac{1}{2})}\left(x\right),\]