As suggested from this topic, we are interested in evaluating the following complex integral

.

The trick here is to use the Fourier transform. Thanks to ZY for teaching me this interesting technique.

In , the Fourier transform of function , denoted by , is defined to be

.

If we apply the Fourier transform twice to a function, we get a spatially reversed version of the function. Precisely,

where denotes the inverse Fourier transform.