\[\operatorname{Hi}\left(z\right)\sim-\frac{1}{\pi z}\sum_{k=0}^{\infty}\frac{(3%
k)!}{k!(3z^{3})^{k}}+\frac{e^{\zeta}}{\sqrt{\pi}z^{1/4}}\sum_{k=0}^{\infty}%
\frac{u_{k}}{\zeta^{k}},\]