File:Diagram of the real branches of the Lambert W function.png

import pylab

from scipy.special import lambertw
from numpy import e, arange, append

pylab.axhline(color="black")
pylab.axvline(color="black")

pylab.grid()

# plot first branch of lambert w function

domain1 = arange(-1/e+0.0000001, 3.001, 0.01)

pylab.plot(domain1, lambertw(domain1, 0), color="blue")
pylab.text(0.2,0.4,"$W_0$", color="blue")

# plot second branch of lambert w function

domain2 = arange(-1/e+0.0000001, -0.02, 0.0001)

pylab.plot(domain2, lambertw(domain2, -1), color="green")
pylab.text(-0.3,-4.5,"$W_{-1}$", color="green")

pylab.savefig("lambertw.png")