TITLE: What is Eulerian?
QUESTION [7 upvotes]: I encountered an interesting function which is called "Eulerian" by the Wolfram's MathWorld:
$$\phi(q)=\prod_{k=1}^{\infty} (1-q^{k})$$
It is interesting because it seems that roots of any polynomial can be expressed in this function and elementary functions.
I want to know more about the properties of this function, where can I find the information?

REPLY [9 votes]: One notable property of this function is Euler's Pentagonal Number Theorem:
$$\prod_{k=1}^\infty (1-x^k) = \sum_{k=-\infty}^\infty (-1)^k x^{k(3k-1)/2}.$$
Here is a very interesting paper on the Pentagonal Number Theorem by Jordan Bell.