File:Langevin+expansions.svg
Summary
| 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 |
This W3C-unspecified plot was created with Gnuplot.Category:Unspec SVG created with Gnuplot#00100308Langevin+expansions.svg
Gnuplot source
#!/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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