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