\[\operatorname{Gi}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-%
\tfrac{1}{3}t^{3}-\tfrac{1}{2}zt\right)\cos\left(\tfrac{1}{2}\sqrt{3}zt+\tfrac%
{2}{3}\pi\right)\,\mathrm{d}t.\]