File:Langevin+expansions.svg
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Size of this PNG preview of this SVG file: 640 × 480 pixels. Other resolutions: 320 × 240 pixels | 1,024 × 768 pixels | 1,280 × 960 pixels | 2,560 × 1,920 pixels.
Original file (SVG file, nominally 640 × 480 pixels, file size: 15 KB)
Captions
Captions
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Summary
[edit]| Description |
English: The Langevin function (red) and two approximations for small x: a truncation of it's continued fraction expansion (green), and a truncation of it's Taylor series (blue) Français : Fonction de Langevin (rouge), avec deux approximations pour des petits x : développement en fraction continue tronqué (vert), et développement limité à l'ordre 3 (en bleu) |
| Date | |
| Source | Own work |
| Author | Edgar Bonet |
Gnuplot source
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#!/usr/bin/gnuplot
# Langevin function and two expansions
set term svg size 640, 480 enhanced font "Times,13"
set output "langevin+expansions.svg"
set xlabel "x" offset 0, 0.5
set xrange [-12:12]
set xtics ("−10" -10, "−5" -5, 0, 5, 10)
set yrange [-1:1]
set ytics ("−1" -1, "−0,5" -0.5, 0, "0,5" 0.5, 1)
set lmargin 6
set grid lt 1 lc rgbcolor "#cccccc"
set key top left Left reverse invert spacing 1.3 width -5
set samples 200
set style line 3 lw 3.0 lc rgbcolor "#cc0000"
set style line 2 lw 1.5 lc rgbcolor "#00ff00"
set style line 1 lw 1.5 lc rgbcolor "#9999ff"
set style increment user
plot x/3 - x**3/45 title "x/3 − x³/45", \
x/(3 + x*x/5) title "x/(3 + x²/5)", \
x==0 ? 0 : 1/tanh(x)-1/x title "L(x)"
Licensing
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I, the copyright holder of this work, hereby publish it under the following license:
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.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:52, 22 October 2013 | | 640 × 480 (15 KB) | Edgar.bonet (talk | contribs) | User created page with UploadWizard |
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- Usage on fr.wikipedia.org
