(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Stirling's Approximation Problem

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