I am looking for class of functions $\cal F$ s.t., for a function $f(x)\in \cal F$ we can express $$\prod\limits_{k<j}(1-f(n)/f(k))$$ in closed form. Few things:
- $n,k,j\in \mathbb{Z}$
- The function is defined on integer space ($f:\mathbb{Z}\mapsto \mathbb{R}$)
- $f(n)\le f(k)\forall k\in (0,j)$
- What I mean by closed form is, we can write $$g(j,n)=\prod\limits_{k<j}(1-f(n)/f(k))$$ where in final expression we do not have $\Pi$.
- To relax question a little- I am looking for some $f(x)$ which follows the property mentioned above.