11/07/2007, 12:12 AM

Ivars Wrote:But, if I understand correctly ( probably not) the picture 4. in the article http://www.cs.uwaterloo.ca/research/tr/1993/03/W.pdf if

nice coincidence. I found a formula in this paper, which agrees perfectly with my fixpoints-for-real-bases b>e^(1/e) formula. In that article they discuss boundaries for the lambert-w-function such that

x = eta ctg(eta) + i * eta

and similar (page 15, formula 4.1 - 4.5)

For the complex fixpoints for real b>e^(1/e) I had the same type of formula; such that

u = beta cos(beta)/sin(beta) + I * beta

t = exp(u)

b = exp(u/t) is real

and this last expression is a branch-enabled version of

b = t^(1/t)

Nice...

Gottfried

Gottfried Helms, Kassel