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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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)
Ah, yeah when I look at that closely it works. Thanks
Originally Posted by SworD 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. Expand the argument to its Taylor series and then let = =
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?
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