Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Universal uniqueness criterion?
#46
@Kouznetsov: how are the other tetrations relevant to our discussion of uniqueness?

@Kouznetsov: Also I just have a quick question to ask about tetration: What is the mathematical reason that the tetrational approaches the fixed points or as you go to ? I think instead, that or , where c is a nonzero real number, should be the limit that corresponds to the fixed point. (when the imaginary part is zero this doesn't work)
Why is this intuitive reasoning incorrect?:
to get from 1 to a non-real number by iteration of exp, you need complex iteration (real iterations always give real numbers)
But then since are repelling with respect to the exponential, you need infinite negative iterations of exp (positive iterations of log). If you infinitely iterate log on a nonreal number, you get closer to L, why isn't this reflected in the tetrational graph? Bo said something like log is not in the initial region anymore, could you clarify that for me? I have attached a schematic diagram to represent my reasoning:
   
how does the tetrational for base b>exp(1/e) actually behave at large values of real part of non-real arguments?
Reply


Messages In This Thread
Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM
Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM
RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM
RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM
RE: Universal uniqueness criterion? - by Base-Acid Tetration - 06/23/2009, 09:28 PM
RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 1,162 09/19/2017, 09:45 PM
Last Post: tommy1729
  A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 10,153 02/17/2017, 05:21 AM
Last Post: JmsNxn
  Uniqueness of half-iterate of exp(x) ? tommy1729 14 13,686 01/09/2017, 02:41 AM
Last Post: Gottfried
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,420 03/19/2016, 10:44 AM
Last Post: fivexthethird
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,799 11/09/2014, 10:20 PM
Last Post: tommy1729
  Real-analytic tetration uniqueness criterion? mike3 25 19,653 06/15/2014, 10:17 PM
Last Post: tommy1729
  exp^[1/2](x) uniqueness from 2sinh ? tommy1729 1 2,080 06/03/2014, 09:58 PM
Last Post: tommy1729
  Uniqueness Criterion for Tetration jaydfox 9 10,592 05/01/2014, 10:21 PM
Last Post: tommy1729
  Uniqueness of Ansus' extended sum superfunction bo198214 4 6,318 10/25/2013, 11:27 PM
Last Post: tommy1729
  A question concerning uniqueness JmsNxn 3 5,258 10/06/2011, 04:32 AM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)