HP49-50G Lambert function

[Albert Chan]

(10-21-2020 02:54 AM)Albert Chan Wrote:  >>> a = -log(2)/2
>>> 1/eW(a, y=0.2)
0 0.2
1 (0.240506189867-0j)
2 (0.24956480343-0j)
3 (0.24999902269-0j)
4 (0.249999999995-0j)
(4.0000000000000018+0j)

There is a reason I picked guess for y below -a (≈ 0.346574)
If guess is above -a, Newton's formula, y ← (y+a)/(log(y)+1), might converge to e^W₀ (*)
If guess is below -a (but still positive), it always converge to e^W_-1

see plot {(y + -ln(2)/2)/(ln(y)+1), y}, y = 0 .. 1/e

(*) it might still converge to e^W_-1, with iterations involving complex numbers.
First iteration overshooted to y<0, then all iterations turned complex.
I tried it, the cut-off is guess ≈ 0.365414