I stumbled upon this somewhere but didn't know how to prove it.

Anyone have any ideas why this is the case or how to derive it? I suspect it has something to do with the gamma function.

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- September 2nd 2012, 11:28 PMSworDA curious limit
I stumbled upon this somewhere but didn't know how to prove it.

Anyone have any ideas why this is the case or how to derive it? I suspect it has something to do with the gamma function. - September 2nd 2012, 11:47 PMJJacquelinRe: A curious limit
The Stirling's approximation of x! for large x is :

(x^x)*exp(-x)*sqrt((2x+(1/3))*pi) equivalent to (x^x)*exp(-x)*sqrt(2*pi)*sqrt(x) - September 2nd 2012, 11:51 PMSworDRe: A curious limit
Ah, yeah when I look at that closely it works. Thanks

- September 2nd 2012, 11:55 PMMaxJasperRe: A curious limit
- September 3rd 2012, 12:04 AMSworDRe: A curious limit
o.O Could you elaborate on how you arrived at that series? Unless you are extending JJacquelin's answer by inputting Stirling's formula then I'm confused.. and isnt this rather a Laurent series?