Is there a simple form to this product?
$\prod_{n=1}^{\infty}(1-\frac{i.b}{n})$
I know for sure that the gamma function relates to it somehow and it could be represented as a binomial series $1-ib+\frac{ib(ib-1)}{2!}-\frac{ib(ib-1)(ib-2)}{3!}...$, but I'm looking for gamma related identities.
Thanks in advance!