Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
matrix function like iteration without power series expansion
bo198214 Wrote:Guys! That I didnt see that before!

We have a very simple formula for computing the -th iterate of an arbitrary function:

I want to add, that this expression exites me very much.

Just these days I was looking for alternatives (hopefully improvements) of our fractional iteration problem.
I was looking for two aspects
  1. expression of the tetration by its own powertowers instead of powerseries
  2. interpolation not done based on polynomial interpolation of the coefficients of the powerseries but based on an interpolation of gamma
The above formula provides both searched aspects in one shot.

The first is obvious; the idea is that only values are involved, which are provided by the function itself (so, for instance, possibly only of a relevant subset of complex numbers which are accessible by the function and its iterates itself/themselves - hmm, amateurish expressed; I hope the idea behind this can be understood anyway)

The second, because the fractional binomials use gamma of fractional parameters.

So - in my view - this is a big shot...

Gottfried Helms, Kassel

Messages In This Thread
RE: matrix function like iteration without power series expansion - by Gottfried - 07/02/2008, 11:23 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 373 03/21/2020, 08:28 AM
Last Post: Daniel
  New mathematical object - hyperanalytic function arybnikov 4 616 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 557 06/23/2019, 08:24 PM
Last Post: Chenjesu
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 3,277 02/18/2019, 10:34 PM
Last Post: Micah
  Degamma function Xorter 0 1,008 10/22/2018, 11:29 AM
Last Post: Xorter
Question Taylor series of i[x] Xorter 12 12,612 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,419 03/11/2017, 10:22 AM
Last Post: Xorter
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,724 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,782 12/21/2016, 01:27 PM
Last Post: tommy1729
  2 fixpoints related by power ? tommy1729 0 1,569 12/07/2016, 01:29 PM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)