I am curious as to where this identity was originally obtained. Any suggestions?
$$ \frac{1}{\mathop{\Gamma}\nolimits\!\left(1+2\mu\right)2\pi i}\int_{-\infty}^% {(0+)}e^{zt+\frac{1}{2}t^{-1}}t^{\kappa}\mathop{M_{\kappa,\mu}}\nolimits\!% \left(t^{-1}\right)dt=\frac{z^{-\kappa-\frac{1}{2}}}{\mathop{\Gamma} \nolimits\!\left(\frac{1}{2}+\mu-\kappa\right)}\mathop{I_{2\mu}}\nolimits\!% \left(2\sqrt{z}\right) $$