Lambert W function (for HP Prime)

[Albert Chan]

(11-07-2020 07:36 AM)lyuka Wrote:  Calculation result by WolframAlpha --
W0(-1.78) ≈ 0.089218049856209317716109060765294251305387407793167833503833064… + i1.6256236744277681331520891017303249073577948841857860157186500…

This convergence behavior in HOME may be due to the fact that 12 digits are not large enough, but,
it's similar to the behavior when there is a problem with normalize-and-rounding for each numerical calculation.

HOME mode imag part rounded up to is 1.62562367443, error = true - approx ≈ -0.22 ULP
However, imag part ULP is 100 times real part ULP.

HOME> y := 8.92180498562ᴇ−2+1.62562367443*i
HOME> y * e^y
−1.78-4.1692ᴇ−12*i

HOME> y := 8.92180498602ᴇ−2+1.62562367443*i
HOME> y * e^y
−1.78-1.276ᴇ−13*i

It may be why HOME mode iterations gravitate to the second number.