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Does tetration take the right half plane to itself?
#2
Of course, as soon as I post this I've essentially proved it using the Fourier expansion. Now I'm just hoping Sheldon comes on and can enlighten me a bit more as to why this works.


First and foremost



where

and



If is the inverse schroder function, normalized so that , then



where 



and, as Sheldon mentions, but I haven't seen a fully rigorous proof,

for

therefore . Now it follows that



and tetration is contained in a disk about that lies in the right half plane.



NOW, all I need is for . Sheldon has claimed this, but in order to put it in the paper, I'll probably either need to prove it myself, or have a good reference. In a short enough, well thought out manner, that is rigorous enough to put in the finalized version of my paper (credit will be given, of course).
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RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/10/2017, 08:22 PM

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