
weaker version of Stirling's approximation

(Result)


One can prove a weaker version of Stirling's approximation without appealing to the gamma function. Consider the graph of and note that
But
, so
and thus
so
As gets large, the expressions on either end approach , so we have
Multiplying through by and exponentiating, we get

"weaker version of Stirling's approximation" is owned by rm50.


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Crossreferences: graph, gamma function
This is version 4 of weaker version of Stirling's approximation, born on 20061119, modified 20061121.
Object id is 8573, canonical name is WeakerVersionOfStirlingsApproximation.
Accessed 356 times total.
Classification:
AMS MSC:  41A60 (Approximations and expansions :: Asymptotic approximations, asymptotic expansions )   30E15 (Functions of a complex variable :: Miscellaneous topics of analysis in the complex domain :: Asymptotic representations in the complex domain)   68Q25 (Computer science :: Theory of computing :: Analysis of algorithms and problem complexity) 



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