TITLE: How to solve the limit $\lim\limits_{n\to \infty}(1-a)(1-a^2)\cdots(1-a^n)$?
QUESTION [7 upvotes]: Suppose $|a|<1$ be a real number. How to solve the following limit?
$$\lim\limits_{n\to \infty}(1-a)(1-a^2)\cdots(1-a^n).$$

REPLY [5 votes]: This limit is the definition of the Euler function, a special function that doesn't seem to have any nicer closed form.