Let

$$f(\lambda)=\int_{\gamma} e^{\lambda\left(t-t^{3} / 3\right)} d t, \quad \lambda \text { real and positive }$$

where $\gamma$ is a path beginning at $\infty e^{-2 i \pi / 3}$ and ending at $+\infty$ (on the real axis). Identify the saddle points and sketch the paths of constant phase through these points.

Hence show that $f(\lambda) \sim e^{2 \lambda / 3} \sqrt{\pi / \lambda}$ as $\lambda \rightarrow \infty$.