# Stirling's Approximation Problem

1. Dec 7, 2011

### Rockoz

1. The problem statement, all variables and given/known data
Use Stirling's Approximation formula to evaluate the following:
1) Γ(12.3) where Γ(N) is the gamma function
2) (π^2)! This is suppose to be pi squared
3) (1/2)!

2. Relevant equations
So here is Stirling's approximation formula:

N! ~= sqrt(2πN)(N/e)^N (where ~= means approximately equal to). And this is accurate to at least two decimal places for N >= 9.

3. The attempt at a solution
For the first problem I am unsure about what to do. I found a formula that says Γ(n) = (n-1)! but I'm not sure if this is only valid for integers. Can I simply plug into stirling's approximation formula (n-1) or in this case (12.3 - 1) = 11.3 to obtain the approximation for Γ(12.3)? For the other two problems do I simply plug in pi^2 and (1/2) into the formula? I apologize if this seems overly simple but this my first time ever seeing this formula and want to make sure I know how to use it in general. Thank you very much to anyone who can help.

2. Dec 8, 2011

### Simon Bridge

That version is only valid for positive integers.

The Gamma function is more broadly defined for complex numbers other than non-positive integers.

Once you have the Stirling approximation to the gamma function, you can use it to evaluate the rest.... it's not just a matter of blindly plugging the number into the equation, you have to make the number the right kind to fit.