# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'lambert.1.png'
set arrow 1 from -0.367879, graph 0, 0 to -0.367879, -1.00000, 0.00000 nohead back nofilled lt 0 linecolor 0 linewidth 1.000 dashtype solid
set samples 1000, 1000
set style data lines
set xzeroaxis
set yzeroaxis
set xtics  norangelimit 0.00000,0.5 
set xtics add  ("-1/e" -0.367879)
set title "real-valued range of Lambert W function for branches k=0 k=-1" 
set xrange [ -1.00000 : 3.00000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ -4.00000 : 2.00000 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
NO_ANIMATION = 1
plot sample [x = -1./e : 4.] LambertW(x, 0) lw 2, [x = -1./e : 0] LambertW(x,-1) lw 2