\[\operatorname{Bi}'\left(ze^{\pm\pi i/3}\right)\mathrel{\sim}\sqrt{\frac{2}{\pi%
}}e^{\mp\pi i/6}z^{1/4}\*\left(-\sin\left(\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}%
\mathrm{i}\ln 2\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{v_{2k}}{\zeta^{2k}}+%
\cos\left(\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}\mathrm{i}\ln 2\right)\sum_{k=0}%
^{\infty}(-1)^{k}\frac{v_{2k+1}}{\zeta^{2k+1}}\right),\]