\[\Psi^{(\mathrm{H})}\left(\mathbf{x}\right)=4\sqrt{\ifrac{\pi}{6}}\,\exp\left(i%
\left(\tfrac{1}{27}z^{3}+\tfrac{1}{6}z(y+x)+\tfrac{1}{4}\pi\right)\right)\*%
\int_{\infty\exp\left(5\pi i/12\right)}^{\infty\exp\left(\pi i/12\right)}\exp%
\left(i\left(2u^{6}+2zu^{4}+\left(\tfrac{1}{2}z^{2}+x+y\right)u^{2}-\frac{(y-x%
)^{2}}{24u^{2}}\right)\right)\,\mathrm{d}u,\]