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