I was looking into the factorial function in an R package called gregmisc and came across the implementation of the gamma function, instead of a recursive or iterative process as I was expecting. The gamma function is defined as:
$$ \Gamma(z)=\int_{0}^{\infty}e^{-t}t^{z-1}dt $$
A brief history of the function points to Euler's solution to the factorial problem for non-integers (although the equation above is not his). It has some application in physics and I was curious if it is useful to any quant models, apart from being a fancy factorial calculator.