File:Legendre's constant 10 000 000.svg
Size of this PNG preview of this SVG file: 694 × 332 pixels. Other resolutions: 320 × 153 pixels | 640 × 306 pixels | 1,024 × 490 pixels | 1,280 × 612 pixels | 2,560 × 1,225 pixels.
Original file (SVG file, nominally 694 × 332 pixels, file size: 136 KB)
File information
Structured data
Captions
Summary
editDescriptionLegendre's constant 10 000 000.svg |
English: The first 10, 000 000 elements of the sequence a_n = \ln(n) - \frac{n}{\pi(n)} (red line), where π is the prime-counting function. Adrien-Marie Legendre conjectured in 1808 that this sequence would converge to a value of approximately 1.08366 (blue line), which became known as Legendre's constant. The actual limit was later shown to be exactly 1. |
||||
Date | |||||
Source |
Plotted in Maple and converted to SVG format in Inkscape by Sandrobt, using the following Maple code: > with(numtheory); > with(plots); > b := vector(10000, proc (i) options operator, arrow; [1000*i, 1.08366] end proc); > c := vector(10000, proc (i) options operator, arrow; [1000*i, 1] end proc); > a := vector(10000, proc (i) options operator, arrow; [1000*i, evalf(log(1000*i)-1000*i/pi(1000*i))] end proc); > display(plot(b, color = blue, thickness = 3), plot(a, color = red), plot(c, color = black, thickness = 3), view = [1 .. 10000000, .95 .. 1.1]); |
||||
Author | Sandrobt | ||||
Other versions |
|
||||
SVG development InfoField | This vector image was created with Inkscape, or with something else. |
Licensing
editI, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- 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.
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 17:40, 2 September 2010 | 694 × 332 (136 KB) | Sandrobt (talk | contribs) | {{Information |Description={{en|1=The first 10, 000 000 elements of the sequence a_n = \ln(n) - \frac{n}{\pi(n)} (red line), where π is the prime-counting function. Adrien-Marie Legendre conjectured in 1808 that this sequence would converge to a value of |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on cs.wikipedia.org
- Usage on en.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ja.wikipedia.org