Stirling's Formula for Gamma Function

Theorem
Let $\Gamma$ denote the Gamma function.

Then:


 * $\map \Gamma {x + 1} = \sqrt {2 \pi x} \, x^x e^{-x} \paren {1 + \dfrac 1 {12 x} + \dfrac 1 {288 x^2} - \dfrac {139} {51 \, 480 x^3} + \cdots}$

Also known as
This formula is also known as Stirling's asymptotic series.