\[\operatorname{Ai}\left(-x\right)=\frac{x^{\ifrac{1}{2}}}{\pi}\int_{-1}^{\infty%
}\cos\left(x^{\ifrac{3}{2}}(\tfrac{1}{3}t^{3}+t^{2}-\tfrac{2}{3})\right)\,%
\mathrm{d}t,\]