\[\operatorname{ker}_{\nu}\left(\nu x\right)+i\operatorname{kei}_{\nu}\left(\nu x%
\right)\sim e^{-\nu\xi}\left(\frac{\pi}{2\nu\xi}\right)^{\ifrac{1}{2}}\left(%
\frac{xe^{3\pi i/4}}{1+\xi}\right)^{-\nu}\sum_{k=0}^{\infty}(-1)^{k}\frac{U_{k%
}(\xi^{-1})}{\nu^{k}},\]