\[\int_{0}^{z}\operatorname{Hi}\left(-t\right)\,\mathrm{d}t\sim\frac{1}{\pi}\ln z%
+\frac{2\gamma+\ln 3}{3\pi}+\frac{1}{\pi}\sum_{k=1}^{\infty}(-1)^{k-1}\frac{(3%
k-1)!}{k!(3z^{3})^{k}},\]