[Fractint] Lambert W

This is a late night , early morning , endeavour ; therefore not as well investigated as usual. There are fractals for the power tower however there didn't appear to be anything for the basic Lambert W function. LamW(XAXIS) {; Edward Montague (c) 2017 ; ; Checked for complex values with Maxima ; ; Lambert's W function via Halley's root finding ; algorithm , with addition imaginary constant . ; ; ; c = z = Pixel w=0.1 : wold=w w=w - (w*exp(w) - z)/((exp(w)*(w+1)-(w+2)*(w*exp(w)-z)/(2*w+2))+(0,0.000001)) .000001 < |w-wold| ; && |w|