Using \(N! = \displaystyle \int_0^{\infty} x^N e^{-x} dx\) (which you can prove by induction), derive Stirling's formula,

\[N! \approx N^N e^{-N} \sqrt {2 \pi N}.\]

Using \(N! = \displaystyle \int_0^{\infty} x^N e^{-x} dx\) (which you can prove by induction), derive Stirling's formula,

\[N! \approx N^N e^{-N} \sqrt {2 \pi N}.\]

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TopNewestWikipedia page on Laplace's method has an answer. – Haroun Meghaichi · 3 years, 2 months ago

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