I'm using the term factorial function as $\gamma(x+1)$ on the sense that I'm taking all real number in count.
I have seen many approximations of the factorial function for positive values, for example the Stirling approximation which starts approaching the function after 1 and the Ramanujan approximation which is very close for all positive $x$.
But I've never seen an approximation that works with negative values. I was wondering if anyone know one, it would be even better if it was on a closed form.
Any thoughts would be really appreciated!!