|This article/section deals with mathematical concepts appropriate for a student in late high school or early university.|
The Gamma funciton is defined as
Relations and values
Using integration by parts,
At , goes to 0. Using L'Hopital's rule, it's easy to show that .
Using this, and the the fact that , then we can get the factorial function. For a positive integer,
where in the last line we used the fact that is an even function. The integral is called the Gaussian integral and has a well known value of .