\[\operatorname{bei}_{\frac{1}{2}}\left(x\sqrt{2}\right)=\frac{2^{-\frac{3}{4}}}%
{\sqrt{\pi x}}\left(e^{x}\sin\left(x+\frac{\pi}{8}\right)+\,e^{-x}\sin\left(x-%
\frac{\pi}{8}\right)\right).\]