\[\operatorname{Ai}'\left(-z\right)\sim\frac{z^{1/4}}{\sqrt{\pi}}\left(\sin\left%
(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{v_{2k}}{\zeta^{2%
k}}-\cos\left(\zeta-\tfrac{1}{4}\pi\right)\sum_{k=0}^{\infty}(-1)^{k}\frac{v_{%
2k+1}}{\zeta^{2k+1}}\right),\]