Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
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).
Reply


Messages In This Thread
RE: Does tetration take the right half plane to itself? - by JmsNxn - 05/10/2017, 08:22 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 386 09/09/2019, 10:55 PM
Last Post: tommy1729
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 623 09/09/2019, 10:50 PM
Last Post: tommy1729
  Half-iteration of x^(n^2) + 1 tommy1729 3 4,156 03/09/2017, 10:02 PM
Last Post: Xorter
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 15,335 01/09/2017, 02:41 AM
Last Post: Gottfried
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 39,181 03/27/2015, 11:28 PM
Last Post: tommy1729
  [entire exp^0.5] The half logaritm. tommy1729 1 2,511 05/11/2014, 06:10 PM
Last Post: tommy1729
  Does the Mellin transform have a half-iterate ? tommy1729 4 3,888 05/07/2014, 11:52 PM
Last Post: tommy1729
  Simple method for half iterate NOT based on a fixpoint. tommy1729 2 3,418 04/30/2013, 09:33 PM
Last Post: tommy1729
  half-iterates of x^2-x+1 Balarka Sen 2 4,167 04/30/2013, 01:14 AM
Last Post: tommy1729
  Is the half iterate of 2sinh(x) analytic near R ? tommy1729 1 2,514 03/13/2013, 12:13 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)