Euler phi

The Euler phi function is defined for $q \in \mathbb{C}$ with $|q|<1$ by $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$

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  Graph of $\phi$.

• Complex qpochhammer (q,q) infty.png

  Domain coloring of analytic continuation of $(q,q)_{\infty}$ to the unit disk.

Properties

Relationship between Euler phi and q-Pochhammer