I've encountered a problem in my PhD. I would greatly appreciate any suggestions, tips, or comments you might have. The problem is

Let $\Gamma(s,x)$ be the incomplete gamma function. Given integers $n > m$, there exist functions $f,g$ such that

$$ \Gamma(n,m) = f(n)g(m) ? $$

In other words, can we separate Gamma in two independent functions, in this specific case?