Factorial
for integers, Factorial $x! = x\, (x - 1)!$ what if $x$ is not an integer?
can use the Gamma Function:
$x! = \Gamma(x) = \int\limits_{t=0}^\infty t^x\, e^{-t}\, dt$
Stirling Formula
Very useful in Probability
$\ln (x!) = x\, \ln x - x + O(\ln x)$ $x! = \sqrt{2\pi x}\, \left( \cfrac{x}{e} \right)^x\, \left( 1 + O(\cfrac{1}{x}) \right)$