Euler phi

The Euler phi function is defined as $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$

• Qpochhammer(q,q)infty.png

  Plot of $(q,q)_{\infty}$ for $q \in [-1,1]$.

• 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