Difference between revisions of "Euler phi"
From specialfunctionswiki
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| − | The Euler phi function is defined | + | The Euler phi function is defined for $q \in \mathbb{C}$ with $|q|<1$ by |
$$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$ | $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$ | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File: | + | 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. | File:Complex qpochhammer (q,q) infty.png|[[Domain coloring]] of [[analytic continuation]] of $(q,q)_{\infty}$ to the unit disk. | ||
</gallery> | </gallery> | ||
Revision as of 03:28, 22 June 2016
The Euler phi function is defined for $q \in \mathbb{C}$ with $|q|<1$ by $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$
Graph of $\phi$
- Complex qpochhammer (q,q) infty.png
Domain coloring of analytic continuation of $(q,q)_{\infty}$ to the unit disk.
