How was Stirling's approximation derived?

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SUMMARY

Stirling's approximation is mathematically expressed as x! ~ sqrt(2πx) (x/e)^x. This approximation provides a method for estimating factorials for large values of x. The derivation of Stirling's approximation can be found in detail in the article referenced from Mathworld, which outlines the step-by-step process. The discussion highlights the utility of this approximation in simplifying calculations involving large factorials.

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Paradox
I was wondering how Stirling's approximation

x! ~ sqrt(2[pi]x)xxe-x

was derived. Anyone know?
 
Mathematics news on Phys.org
This article at Mathworld derives Stirling's approximation step by step. :smile:
 
Thanks for the link, Jeff. It helped a lot :smile:
 

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