I have just looked at the gamma function and am wondering what it tells us and what is the point in the function?

The Euler Gamma function can be thought of as the extension of the factorial function to complex arguments.

 

The gamma function crops up in many different areas of mathematics. For example, the gamma function arises when calculating the volume of a n-sphere.

 

Have a look here for more details

 

http://mathworld.wolfram.com/GammaFunction.html

As ajb said, it's the extension of the factorial function to the complex plane. There's a number of useful identities that you can find at the MathWorld page to do with dilogarithms and the like. I suggest you look at related functions as well, as there's really a whole bunch of them and it can be more interesting to look at the group of them rather than single out the gamma function.

There are physical problems where the solution involves gamma functions, too. Many diffusion problems have gamma function or error function solutions. While it is not introduced at the same time as sine or cosine, etc., I think of them as just another useful, well-studied, tabulated function that just comes up. Bessel functions are another example of functions that just arise naturally when describing some physical situations.

Bignose is right.

 

One appliction of the gamma function is in the path integral formulation of quantum field theory. I am sure there are many many other situations in which the gamma function comes up.

Thanks guys!