I was thinking about probability games when I stumbled upon an interesting sequence, namely
$$\prod_{k=1}^\infty{(1-q^k)} = (1-q)(1-q^2)(1-q^3)...$$
I was specifically interested in a proof on whether this function converges to a non-zero value for all $q \in \mathbb{C},\ |q| < 1$.
A quick google search pointed me to Wiikipedia's "Euler function" entry, which is exactly the function I'm looking for. However, the page lacks any links to helpful online results or resources, only referencing a couple of hardcover books and OEIS (and surprisingly a paper in German?).
Unfortunately, searching Euler's function doesn't give any relevant results as it's understandably overwhelmed by Euler's more famous (totient) function.
I'm really at a loss here, as my only lead seems to be a dead end.
Does anyone know any online resources regarding this function, or a better way to search for references specifically about this Euler's function?
Thanks in advance.