Tetration Forum › Tetration and Related Topics › Mathematical and General Discussion v
A tiny base-dependent formula for tetration (change-of-base?)

Linear Mode
A tiny base-dependent formula for tetration (change-of-base?)
Gottfried Offline
Ultimate Fellow
*****
Posts: 904
Threads: 131
Joined: Aug 2007
#8
03/17/2009, 06:36 PM (This post was last modified: 12/30/2017, 09:20 PM by Gottfried.)
Hmm, curious... curious... ,

things evolve a bit more. From the tetrated pascalmatrices we can also derive a fractional iteration if we apply the binomial-formula to the sequence of powerseries for different heights. Since the powerseries have this stunning smooth behave for increasing heights, the binomially interpolated series are accordingly smooth.
This seems all to be too crazy.... very smooth for the convergence bases and possibly continuable for the divergent cases, don't see it yet.

See the new chapter 2 in
PascalmatrixTetrated

Gottfried
Gottfried Helms, Kassel
Website Find
Reply


Messages In This Thread
RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/17/2009, 06:36 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Mixed-base tetration: five preprints, a faster fatou.gp fork, and a base-change calcu Lightrunner 0 200 07/15/2026, 08:33 AM
Last Post: Lightrunner
  Seeking an arXiv endorser for mixed-base tetration (math.DS) Lightrunner 0 164 07/13/2026, 10:19 PM
Last Post: Lightrunner
  [2sinh] exp(x) - exp( - (e-1) x), Low Base Constant (LBC) 1.5056377.. tommy1729 3 6,727 04/30/2023, 01:22 AM
Last Post: tommy1729
  f(x+y) g(f(x)f(y)) = f(x) + f(y) addition formula ? tommy1729 1 3,733 01/13/2023, 08:45 PM
Last Post: tommy1729
  Base -1 marraco 15 40,490 07/06/2022, 09:37 AM
Last Post: Catullus
  I thought I'd take a crack at base = 1/2 JmsNxn 9 16,071 06/20/2022, 08:28 AM
Last Post: Catullus
Question Formula for the Taylor Series for Tetration Catullus 8 15,598 06/12/2022, 07:32 AM
Last Post: JmsNxn
Big Grin Repetition of the last digits of a tetration of generic base Luknik 12 22,664 12/16/2021, 12:26 AM
Last Post: marcokrt
  On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e JmsNxn 0 3,935 09/28/2021, 05:44 AM
Last Post: JmsNxn
  A different approach to the base-change method JmsNxn 0 4,303 03/17/2021, 11:15 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)