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Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
#17
Ivars Wrote:However, as e^-pi/2 > e^-e,

h(e^-pi/2) = 0,474541.......= (2/pi)*W(pi/2)

So there is no symmetry and i will not be a result of analytic continuation of infinite tetration of anything, while -i is.

This depends on how you analytically continue h, on which path.
W (and hence h) has a singularity at , so if you continue on different paths around , you possibly get different results (similar to the analytic continuation of the logarithm with singularity at 0).
Surely on another path/branch
.

Edit: Perhaps its not at all "Surely", was just my conjecture.
Edit2: Now its not a conjecture anymore but regarded as nonsense XD, instead on another branch.
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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 bo198214 - 11/03/2007, 12:54 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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