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