\[\operatorname{ker}_{\nu}'x\sim-e^{-x/\sqrt{2}}\left(\frac{\pi}{2x}\right)^{%
\frac{1}{2}}\sum_{k=0}^{\infty}\frac{b_{k}(\nu)}{x^{k}}\*\cos\left(\frac{x}{%
\sqrt{2}}+\left(\frac{\nu}{2}+\frac{k}{4}-\frac{1}{8}\right)\pi\right),\]