Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
tetration base conversion, and sexp/slog limit equations
#14
sheldonison Wrote:

A very appealing formula (though the two limits belong to the right side of the equal sign)!

For my taste, if I rewrite and generalize your formula a bit ad hoc (dont know whether it is true in that form):



has a big similarity to Zdun's [1] formula for regular iteration (where is assumed to have fixed point at 0):

, .

Only is replaced by . But be aware that , which makes the similarity even more striking.

[1] Zdun, Marek Cezary. Regular fractional iterations. Aequationes Math. 28 (1985), no. 1-2, 73--79. MR0781210
Reply


Messages In This Thread
RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/24/2009, 09:57 PM
Is it analytic? - by sheldonison - 12/22/2009, 11:39 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 1,310 08/14/2019, 09:15 AM
Last Post: sheldonison
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,231 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 1,469 09/06/2016, 04:23 PM
Last Post: tommy1729
  Taylor polynomial. System of equations for the coefficients. marraco 17 15,345 08/23/2016, 11:25 AM
Last Post: Gottfried
  Dangerous limits ... Tommy's limit paradox tommy1729 0 1,772 11/27/2015, 12:36 AM
Last Post: tommy1729
  tetration limit ?? tommy1729 40 44,382 06/15/2015, 01:00 AM
Last Post: sheldonison
  Some slog stuff tommy1729 15 11,324 05/14/2015, 09:25 PM
Last Post: tommy1729
  Totient equations tommy1729 0 1,649 05/08/2015, 11:20 PM
Last Post: tommy1729
  Bundle equations for bases > 2 tommy1729 0 1,662 04/18/2015, 12:24 PM
Last Post: tommy1729
  Limit of mean of Iterations of f(x)=(ln(x);x>0,ln(-x) x<0) =-Omega constant for all x Ivars 10 13,983 03/29/2015, 08:02 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)