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