Find the Taylor and Maclaurin series of the given function with the given point $\displaystyle z_0$ as center and determine the radius of convergence.

$\displaystyle e^{\frac{z^2}{2}}\int e^{-t^2} dt$

By the way, integrate from 0 to z and center at $\displaystyle z_0 = 0$

I cannot imagine, how can I solve this.