Question: What are the typical methods used to compute Fourier transforms for probability type integrals?
There are so many different techniques for integration, but since probability integrals seem to be mostly of a certain type (eg. they concern algebraic, exponential, and special functions) I figure there should probably be some methods that are used over and over again. What are they?
Note: I have had first courses on complex analysis, harmonic analysis and probability theory. I am looking for a collection of techniques to learn about so I can tackle more and more of these types of integrals on my own. A big picture overview would be nice too.
As it stands now, I just eventually give up and ask on here, but I would like to sort of get an idea of which techniques to try, so I can extend the time it takes to give up and have some general idea about where the answers I receive here fit.