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Does tetration take the right half plane to itself?
(05/16/2017, 03:34 PM)sheldonison Wrote:
(05/16/2017, 04:09 AM)JmsNxn Wrote: ...  It easily follows from this that is fully monotone, it uniformly converges to the inverse Schroder function, and therefore the inverse Schroder function is a fully monotone function...
Good luck with your paper.  We need more rigorous iterated exponentiation papers.
I just wondered what your approach to show the sequence "uniformly converges".  Is there an easy theorem, or did you want to go with a more complicated approach something like my lemma5?  Just curious.  Also, you probably meant   where b is the tetration base.

Yeah, I meantt . This is actually a well known result on how to represent the inverse Schroder function. Bo used it before, and that's how I first learnt about it. 

Essentially if

and , then not only does

for , where is the Schroder function. 

We also get that, if

for , for sufficiently small. This is all you really need.

Messages In This Thread
RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/16/2017, 08:46 PM

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