\[\Psi^{(\mathrm{H})}\left(\mathbf{x}\right)=\frac{2\pi}{3^{1/3}}\int_{\infty%
\exp\left(5\pi i/6\right)}^{\infty\exp\left(\pi i/6\right)}\exp\left(i(s^{3}+%
xs)\right)\operatorname{Ai}\left(\frac{zs+y}{3^{1/3}}\right)\,\mathrm{d}s.\]