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Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
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Ivars Wrote:The initial spider graph of Gottfried looks very much like Caley transform, except that it is has 2 conjugate angled maps of slightly elongated circles, and the lines that should be inside Unit circle in Cayleys transform have moved to the negative part of real axis.

http://mathworld.wolfram.com/CayleyTransform.html

What transform would produce such a map from real axis as Gottfrieds spider?

By the way, the result h(e^pi/2) = +-i also is a result of transform (e^pi/2)^ ((i-1/i+1)) and (e^pi/2)^((-i+1)/(-i-1))

Here the angle by which reals are turned is +-pi/2. As the values go above e^pi/2, angles increase but later decrease again. So the transform is definitely more complex than just:

e^Real^((i-Real)/(i+Real) which is true in case Real=e^pi/2.

Hi Ivars -

please have a look at Henryk's curve; I think it is much better.
http://math.eretrandre.org/tetrationforu...931#pid931
(sorry, I'm fully engaged with the tetra-series-problem, which drives me crazy (but makes me learn a lot), such that I've currently no room for other discussion ... :-( )


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 - 12/30/2007, 05:33 PM
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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