(28/48/50) Lambert W Function

[Albert Chan]

(03-22-2023 07:30 PM)John Keith Wrote:  y = sqrt(1+e*x)
...
With 'a' determined empirically to be 2.036, final formula is:

-1 + 2.036*ln((1 + 1.14956131*y)/(1 + 0.4549574*ln(1 + y))

Recurrence from same paper, also from "Guaranteed- and high-precision
evaluation of the Lambert W function" by Lajos Lóczi.

B'(x) = (B(x)/(1 + B(x))*(1 + ln(x/B(x))

There is a flaw with Iacono and Boyd W guess formula.
If x is tiny enough, below 6e-10, it could return a negative guess.
This cause Newton formula to take a log of negative number, which crash it.