Proving Stirling's formula.. help

1. Physicist

43
proving Stirling's formula.. help plz

How can I prove Stirling's formula?

n!= integral from 0 to inf. exp(-t) t^n dt= n^n exp(-n) (2 pi n)^0.5

there's a hint to use the substitution t=ny & ln(1+y) = y- 0.5 y^2

I tried to use it but I couldn't intgrate.. I tried integrating by parts but it became more complicated..

Can anyone help?

(How can I write the mathematical symbols here?)

Thanks

Last edited: Nov 26, 2004
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3. Andrew Mason

6,834
Try:
http://www.sosmath.com/calculus/sequence/stirling/stirling.html

AM

4. Tide

3,143
Another approach would be to use the method of steepest descent. Basically, you can find where $t^n e^{-t}$ is a maximum and observe that the most significant contribution to the integral comes from near that maximum.

5. Physicist

43
Thanks for helping.. but I should uuse the substitution t=ny..

HELP PLZ

2,537
7. Physicist

43
Thanks alot..

8. nafaa

7
Re: proving Stirling's formula.. help plz

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