Summary

DescriptionQ-Eulero.jpeg	English: This picture shows the modulus ${\displaystyle |\phi (q)|}$ on the complex plane, inside the unit circle ${\displaystyle |q|\leq 1}$, where ${\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k})}$ is Euler's q-series for the Partition of an integer. The fractal self-similarity of this function is that of the modular group; note that this function is closely related to a modular form, the modular discriminant. Every modular function will have this general kind of self-similarity. It is colored with a rainbow of colors, with black representing values near zero, and red values near four. Note the Modular group symmetry, and the general resemblance to colorings of the interior of the Mandelbrot set. Italiano: L'immagine mostra il modulo ${\displaystyle |\phi (q)|}$ nel piano complesso, all'interno del cerchio unitario ${\displaystyle |q|\leq 1}$, dove ${\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k})}$ è la q-serie di Eulero per la partizione di un intero.
Date	2 January 2005 (original upload date)
Source	Own work (Original caption: " Created by Linas Vepstas User:Linas <linas@linas.org> on 2 January 2005 using custom software written entirely by Linas Vepstas. ")
Author	Linas Vepstas      Alternative names L. Vepstas Description technologist, entrepreneur, researcher, programmer and computer scientist GnuCash maintainer for over 7 years. Authority file : Q61131517 VIAF: 311397845 ORCID: 0000-0002-2557-740X creator QS:P170,Q61131517
Permission (Reusing this file)	Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

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Original upload log

• 2005-01-02 17:47 Linas 600×600× (26623 bytes) Euler's q-series on the complex plane

• 2011-01-31 21:39 Filippo Colantuono 600×600× (26623 bytes) {{Informazioni file |Descrizione = L'immagine mostra il modulo <math>| \phi(q) |</math> nel piano complesso, all'interno del cerchio unitario <math>|q| \le 1</math>, dove :<math>\phi(q)=\prod_{k=1}^\infty (1-q^k)</math> è la q-serie di Eulero per la [[partizione di un intero]]. |Fonte = Opera creata da [http://en.wikipedia.org/wiki/User:Linas User:Linas] (Linas Vepstas) |Data = 2 Gennaio 2005 |Autore = [http://en.wikipedia.org/wiki/User:Linas User:Linas] (Linas Vepstas) |Licenza = {{GFDL-with-disclaimers|migration=relicense}} |Detentore copyright = [http://en.wikipedia.org/wiki/User:Linas User:Linas] (Linas Vepstas) |EDP = |Altre versioni = }}