I Integration leading to ERFI solutions

Tags:
1. Mar 25, 2016

Oaxaca

I am attempting to normalize a wave function and need to integrate $\int A^2*e^{(\lambda^2x^2)} dx$ going from -inf to +inf. I tried to integrate this on Wolfram Alpha and this was the result. Upon integrating with the parameters the solution is as such. How does the erfi get removed? Do I need to be familiar with the Dawson function?

Thank you for any help!

2. Mar 25, 2016

JorisL

If you look at the condition for the case when there is no inverse error function (erfi) you'll see that they require
$$Re(\lambda^2)<0$$

This means that we can choose $\lambda=i C$ (for simplicity).

Do you see what happens in that case?