Question

What is the difference between the factorial and the gamma function?

Answer 1

The gamma function is kindof a generalization of the exponential function. For any integer, G(n+1) = n! ; however, the gamma function is defined over (almost) all of the imaginary plane.

Answer 2

so the gamma function is like factorial, but it also works on reals?

Answer 3

Yes, the idea is to fill the gap between the integer value of the factorial. (I.e : http://upload.wikimedia.org/wikipedia/commons/0/08/Factorial_interpolation.png )

Answer 4

You should prove for yourself that
\[\Gamma(n+1) = n!\]
It's a good, easy exercise and a satisfying result.