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.