$\mathrm{Bi}'~(-z)\sim\pi^{-\frac{1}{2}}z^{\frac{1}{2}}\left[\mathrm{sin}\left(\zeta+\dfrac{\pi}{4}\right)\sum\limits_0^{\infty}(-1)^kd_{2k}\zeta^{-2k} -\mathrm{cos}\left(\zeta+\dfrac{\pi}{4}\right)\sum\limits_0^{\infty}(-1)^kd_{2k+1}\zeta^{-2k-1}\right]\qquad(|\mathrm{arg}~z|<\frac{2}{3}\pi)$

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