\[\operatorname{bei}_{\nu}x\sim\frac{e^{x/\sqrt{2}}}{(2\pi x)^{\frac{1}{2}}}\*%
\sum_{k=0}^{\infty}\frac{a_{k}(\nu)}{x^{k}}\sin\left(\frac{x}{\sqrt{2}}+\left(%
\frac{\nu}{2}+\frac{3k}{4}-\frac{1}{8}\right)\pi\right)+\frac{1}{\pi}(\cos%
\left(2\nu\pi\right)\operatorname{ker}_{\nu}x-\sin\left(2\nu\pi\right)%
\operatorname{kei}_{\nu}x).\]