I think you should be familiar with at least some Calculus before trying to get into Complex Analysis. I don't know if you are by the way, I ain't familiar with european education
If it helps, the LT of the error function \frac{2}{\pi^{\frac{1}{2}} }\int_0^t e^{-u^2} du is \frac {1}{s(s+1)^{1/2}}
And since you can always work with the N(0,1) distribution instead of the more general N(m, sigma^2) I think you'll find the aforementioned result useful. If you need the...