Question

GAMMA FUNCTION PROBLEM

Answer 1

The integral in \(\Gamma (p) = \int\limits_{0}^{\infty} x^{p-1} e^{-x} dx \) is improper because of the upper limit and it is also improper for 0 < p < 1. because \(x^{p-1}\) becomes infinite at the lower limit. However, the integral is convergent for any p>0. Prove this!

Answer 2

Here is a relatively easy to follow proof:
http://mathhelpforum.com/calculus/1524-convergence-gamma-function.html