- #1

- 197

- 4

## Homework Statement

We know that

[tex]\int_{-\infty}^\infty e^{-ax^2}dx = \sqrt{\pi \over a}[/tex].

Does this hold even if [tex]a[/tex] is complex?

## Homework Equations

## The Attempt at a Solution

In the derivation of the above equation, I don't see any reason why we must assume that [tex]a[/tex] be real. So I think it does hold for complex [tex]a[/tex].