I want to compute $$\frac{1}{2\pi i}\int^{b+i\infty}_{b-i\infty}e^{z^2}z^{zt}dz$$
At the first glance I thought it's just a routine contour integral thing, but I found that $\left|e^{z^2}z^{zt}\right|$ grows with large $\left|z\right|$ and undefined at infinity. So seems I can't find a good contour. Also I recalled that $\frac{d}{dz}erfi(z)=e^{z^2}$ but it doesn't look like to help.
Those are all my attempts and thank you for your help.