HP49-50G,VER16.2 Lambert Funktion Wk(x), k=k= 0, ±1, ±2, ±3, ±4..., x real or complex

[Gil]

“Technically, W-1(-0.1) does not exist. (we have 2 different limits!)
By convention, we returned W-1(-0.1+0*I), which does exist."

Sorry, but for the interval - 1/e<x<0, doesn't W(k=-1,x) represent —by convention ? — the lower part of the function?

For me, the solution z=(-4.4490981787,-7.30706078926)
is for W{k=-2,-.1) = (-4.4490981787,-7.30706078926).