I have a function of the form:

$f(n) = \prod_{i=1}^{n-1} (1-ai)$

Here, $a \geq 0$ and $(a*i) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that will allow me compute values for the function with reasonable computational resources? What bounds on the error of the approximation can I expect?