File:Q-Eulero.jpeg

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File:Q-Eulero.jpeg - Wikipedia

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Summary

Description

English: This picture shows the modulus

|\phi (q)|

on the complex plane, inside the unit circle

|q|\leq 1

, where

\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

|\phi (q)|

nel piano complesso, all'interno del cerchio unitario

|q|\leq 1

, dove

\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

Permission
(Reusing this file)

Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

Licensing

Linas at the English-language Wikipedia, the copyright holder of this work, hereby publishes it under the following license:

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers.
	Attribution: Linas at the English-language Wikipedia
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.CC BY-SA 3.0truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. Subject to disclaimers.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.

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

The original description page was here. All following user names refer to it.wikipedia.

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 = }}

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	04:18, 1 February 2011		600 × 600 (26 KB)	File Upload Bot (Magnus Manske)	{{BotMoveToCommons\|it.wikipedia\|year={{subst:CURRENTYEAR}}\|month={{subst:CURRENTMONTHNAME}}\|day={{subst:CURRENTDAY}}}} {{Information \|Description={{it\|L'immagine mostra il modulo <math>\| \phi(q) \|</math> nel piano complesso, all'interno del cerchio unita

File usage

The following 4 pages use this file:

Global file usage

The following other wikis use this file:

Usage on de.teknopedia.teknokrat.ac.id
Usage on el.wikipedia.org
- Συνάρτηση ήτα του Ντέντεκιντ
Usage on eo.wikipedia.org
- Funkcio de Euler
Usage on es.teknopedia.teknokrat.ac.id
- Función de Euler
Usage on fa.teknopedia.teknokrat.ac.id
- تابع اویلر
Usage on fr.teknopedia.teknokrat.ac.id
- Fonction d'Euler
- Méthode du cercle de Hardy-Littlewood
Usage on it.teknopedia.teknokrat.ac.id
- Funzione di Eulero (forma modulare)
- Funzione eta di Dedekind
Usage on sv.wikipedia.org
- Dedekinds etafunktion
Usage on uk.wikipedia.org
- Круговий метод Гарді — Літлвуда
Usage on zh.teknopedia.teknokrat.ac.id
- 歐拉函數 (複變函數)

Metadata

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If the file has been modified from its original state, some details may not fully reflect the modified file.

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Summary

Licensing

Original upload log

Captions

Items portrayed in this file

depicts

copyright status

copyrighted

copyright license

GNU Free Documentation License, version 1.2 or later

Creative Commons Attribution-ShareAlike 3.0 Unported

source of file

original creation by uploader

inception

2 January 2005

media type

image/jpeg

File history

File usage

Global file usage

Metadata