Today I Learned

Some of the things I've learned every day since Oct 10, 2016

6: Stirling’s Approximation

Stirling’s Approximation, or Stirling’s Formula, is an approximation of the factorial (!) function, given by

n! \sim \sqrt{2 \pi n}(\frac{n}{e})^n

It was originally suggested by Abraham de Moivre that n! \sim C n^{n + \frac{1}{2}} e^{-n} for some constant C. James Stirling’s contribution was showing that C = \sqrt{2 \pi}.

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