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Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
#33
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
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Messages In This Thread
RE: Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) - by Gottfried - 11/07/2007, 12:12 AM
RE: Tetration below 1 - by Gottfried - 09/09/2007, 07:04 AM
RE: The Complex Lambert-W - by Gottfried - 09/09/2007, 04:54 PM
RE: The Complex Lambert-W - by andydude - 09/10/2007, 06:58 AM

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