\[\operatorname{Hi}\left(z\right)=\frac{3^{-2/3}}{2\pi^{2}i}\int_{-i\infty}^{i%
\infty}\Gamma\left(\tfrac{1}{3}+\tfrac{1}{3}t\right)\Gamma\left(-t\right)(3^{1%
/3}e^{\pi i}z)^{t}\,\mathrm{d}t,\]