Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Does tetration take the right half plane to itself?
#8
(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.
Reply


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

Possibly Related Threads...
Thread Author Replies Views Last Post
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 76 09/09/2019, 10:55 PM
Last Post: tommy1729
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 193 09/09/2019, 10:50 PM
Last Post: tommy1729
  Half-iteration of x^(n^2) + 1 tommy1729 3 3,576 03/09/2017, 10:02 PM
Last Post: Xorter
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 13,422 01/09/2017, 02:41 AM
Last Post: Gottfried
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 34,939 03/27/2015, 11:28 PM
Last Post: tommy1729
  [entire exp^0.5] The half logaritm. tommy1729 1 2,241 05/11/2014, 06:10 PM
Last Post: tommy1729
  Does the Mellin transform have a half-iterate ? tommy1729 4 3,448 05/07/2014, 11:52 PM
Last Post: tommy1729
  Simple method for half iterate NOT based on a fixpoint. tommy1729 2 3,065 04/30/2013, 09:33 PM
Last Post: tommy1729
  half-iterates of x^2-x+1 Balarka Sen 2 3,864 04/30/2013, 01:14 AM
Last Post: tommy1729
  Is the half iterate of 2sinh(x) analytic near R ? tommy1729 1 2,320 03/13/2013, 12:13 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)