# Evaluating integral in terms of Gamma functions

1. Feb 29, 2012

### arex

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

The Gamma function is given by $\Gamma$(x) = 0 tx-1e-t dt

Evaluate 0 exp(-αy2)dy in terms of Gamma functions.

2. Relevant equations

n/a

3. The attempt at a solution

Honestly, I don't know where to start. I have knowledge of parametric differentiation (we use alpha as the variable in class which may hint at its usage here) but I don't immediately see how it would help or what it even means to evaluate the integral "in terms of gamma functions."

I'm not just looking for the answer, I'd like a starting hint or tip to get going.

2. Feb 29, 2012

### Ray Vickson

You obviously need to find some alternative expression for the Gamma function that involves an integration with exp(-y^2) in it.

RGV

Last edited: Feb 29, 2012
3. Feb 29, 2012

### Dick

I think arex can work with that definition. Try the change of variable x=ay^2.