I am working with Whittaker functions for a project and have no experience with asymptotic analysis - how is the following expression, for $\kappa \rightarrow \infty$ through the real numbers \begin{equation}\mathop{W_{\kappa,\mu}}\nolimits\!\left(x\right)=\sqrt{x}\mathop{\Gamma}% \nolimits\!\left(\kappa+\tfrac{1}{2}\right)\left(\mathop{\sin}\nolimits\!% \left(\kappa\pi-\mu\pi\right)\mathop{J_{2\mu}}\nolimits\!\left(2\sqrt{x% \kappa}\right)-\mathop{\cos}\nolimits\!\left(\kappa\pi-\mu\pi\right)\mathop{% Y_{2\mu}}\nolimits\!\left(2\sqrt{x\kappa}\right)+\mathop{\mathrm{env}Y_{2\mu% }}\nolimits\!\left(2\sqrt{x\kappa}\right)\mathop{O}\nolimits\!\left(\kappa% ^{-\frac{1}{2}}\right)\right),\end{equation}
Derived? My goal is to extend this form for $\kappa$ imaginary and see something like an exponential decay.