Difference between revisions of "Euler phi"

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File:Eulerphiplot.png|Graph of $\phi$.
 
File:Eulerphiplot.png|Graph of $\phi$.
File:Complex qpochhammer (q,q) infty.png|[[Domain coloring]] of [[analytic continuation]] of $(q,q)_{\infty}$ to the unit disk.
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File:Complexeulerphiplot.png|[[Domain coloring]] $\phi$.
 
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Revision as of 03:59, 22 June 2016

The Euler phi function (not to be confused with the Euler totient) is defined for $q \in \mathbb{C}$ with $|q|<1$ by $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$

Properties

Relationship between Euler phi and q-Pochhammer

References