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Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
#48
Ivars Wrote:As a conjecture, perhaps h (sqrt2) will have one real value at from ln(sqrt2) and another from ln(-sqrt2).
h(cube root 2) may have 3 values, h(4th root of 2) may have 4 converging values etc.

Ivars -

Hmm, I've not been in your discussion with Henryk (have my mind elsewhere these days) and I don't know, perhaps I'm missing the point.
What is the point of your question - besides, that we have conjugate solutions? If I recall my above graphs, for instance, then they show obviously conjugacy. And my graph for complex fixpoints for real bases b>e^(1/e)

   

can be continued for any number of solutions t and u, where imag(u)=some selection +- 2*k*pi (= beta in the graph). (though changing the k-factor only does not lead exactly to the same b, but this should not be seen as a problem). So there may be some problem, that I'm missing when I read your posts?

Gottfried

graph: alpha + I*beta = u
a +I*b = t = exp(u)
s = exp(u/t) = base-parameter
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 - 11/14/2007, 05:04 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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