# Gamma and Beta Integrals

1. Jun 23, 2011

### Ted123

1. The problem statement, all variables and given/known data

The Gamma and Beta integrals are defined respectively as

$$\Gamma (z) = \int^{\infty}_0 t^{z-1} e^{-t}\;dt$$
$$B(p,q) = \int^1_0 t^{p-1} (1-t)^{q-1}\;dt.$$
Determine for what values of the complex parameters z, p, q the integrals converge absolutely and explain why.

3. The attempt at a solution

How would I do this? Is the answer: $$\text{Re}(z) > 0,\;p,\,q>0\;?$$
If so, how do I show it and explain why?

Last edited: Jun 23, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted