Stirling's Formula

Theorem
The factorial function can be approximated by the formula:
 * $n! \sim \sqrt {2 \pi n} \paren {\dfrac n e}^n$

where $\sim$ denotes asymptotically equal.

Also defined as
This result can also be seen reported as:
 * $n! \sim \sqrt {2 \pi} n^n n^{1/2} e^{-n}$

Other variants are sometimes encountered.

Also known as
Stirling's Formula is otherwise known as Stirling's approximation.

Also see

 * Limit of Error in Stirling's Formula