[Regular tetration] [Iteration series] norming fixpoint-dependencies
(08/30/2010, 11:14 PM)tommy1729 Wrote: i.e. z<> z^z => z^z =/= (z + z^^2)/2.

I explained in an earlier post my misuse of the z^^h-notation. (Oh, that was in the other thread only?, Then - sorry)
Ok. To make ascii-writing short I use it there (and now here) in that meaning:

using a base b, z^^h is b^b^...^b^z where h is the number of b,

in case of continuous: z^^h =

I think that "misuse" can be justified since we usually talk about a fixed chosen base ("b") and discuss the change of parameter z as iteration start, h as iteration "height" and z^^h as iteration result. Reading some "z^z" above I think there is a misunderstanding there.

Gottfried Helms, Kassel
i will explain later ...

( edit ) i started a new thread in the general section related to (mainly) this and my ' f(x) = f(x^2) blunder thread '

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 1,357 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Discussion on "tetra-eta-series" (2007) in MO Gottfried 40 1,342 02/22/2023, 08:58 PM
Last Post: tommy1729
  What are the types of complex iteration and tetration? Daniel 5 835 08/17/2022, 02:40 AM
Last Post: JmsNxn
Question Tetration Asymptotic Series Catullus 18 2,471 07/05/2022, 01:29 AM
Last Post: JmsNxn
Question Formula for the Taylor Series for Tetration Catullus 8 2,295 06/12/2022, 07:32 AM
Last Post: JmsNxn
  Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 17 31,592 06/11/2022, 12:24 PM
Last Post: tommy1729
  Categories of Tetration and Iteration andydude 13 31,784 04/28/2022, 09:14 AM
Last Post: MphLee
  Calculating the residues of \(\beta\); Laurent series; and Mittag-Leffler JmsNxn 0 896 10/29/2021, 11:44 PM
Last Post: JmsNxn
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 823 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Reducing beta tetration to an asymptotic series, and a pull back JmsNxn 2 1,833 07/22/2021, 03:37 AM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)