Plot_of_Lambert_W_function_of_x_exp_x.svg

Summary

Description
English: Plot of and for , where and are the branches of the Lambert W function .
Date
Source Own work
Author Hugo Spinelli
Source code
InfoField
Try it here ( permalink ).
SageMath code 
var('x')
x_min, x_max = -3, 3
x_max2 = N(lambert_w(0, x_min*exp(x_min)))

f1 = lambda x: lambert_w(0, x*exp(x))
f2 = lambda x: lambert_w(-1, x*exp(x))

p = plot(f1, (x_min, x_max), thickness=2, color='blue', legend_label=r'$y = W_0(xe^x)$')
p += plot(f2, (x_min, x_max2), thickness=2, color='red', legend_label=r'$y = W_{-1}(xe^x)$')
config = dict(aspect_ratio=1, axes_labels=['$x$', '$y$'], legend_font_size=16)
show(p, **config)
p.save('Plot_of_Lambert_W_function_of_x_exp_x.svg', **config)

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication .
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Captions

Plot of the Lambert W function of x exp x for each branch.

Items portrayed in this file

depicts

Lambert W function

inception

28 September 2023