Difference between revisions of "Euler phi"
From specialfunctionswiki
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| − | The Euler phi function is defined for $q \in \mathbb{C}$ with $|q|<1$ by | + | The Euler phi function (not to be confused with the [[Euler totient]]) is defined for $q \in \mathbb{C}$ with $|q|<1$ by |
$$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$ | $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$ | ||
Revision as of 03:55, 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 $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$
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
