# 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 $C = \sqrt{2 \pi}$.