Identity for $\displaystyle\prod_{n=n_0}^{n=n_1} (n + a)$ for $a \in\mathbb{R}$

Question

I wish to know if there exists an identity to simplify $$\prod_{n=n_0}^{n=n_1} (n + a)$$ where $n_0\in\mathbb{N}$, $n_1\in\mathbb{N}$, and $a\in\mathbb{R}$ are all constants. If it is of assistance, $n_1 = k n_0$ can be safely taken for $k\in\mathbb{N}$.

I wrote code in sympy and sought to find a pattern that would produce and inductive hypothesis; however, my attempts have been unsucessful.

Answer 1

It is equal to $$\Gamma(n_1 + a +1)/\Gamma(n_0 + a + 1).$$ Whether this is useful or not, I have no way of telling.