Formula for the Taylor Series for Tetration
#9
(06/12/2022, 06:50 AM)Daniel Wrote:
(06/12/2022, 06:33 AM)JmsNxn Wrote:
(06/12/2022, 06:17 AM)Daniel Wrote: See tetration combinatorics for more information. The example derives \( D^4f^n(z) \). The following works for all smooth iterated functions, so it applies to tetration and the hyperoperators.
Enumerate the total partition of 65536 (not computationally practical), evaluate each enumeration and add the terms together.

Hey, Daniel. Catullus was asking about Kneser. This does not solve Kneser. This only solves the geometric solution about a Fixed point (Schroder iteration).
JmsNxn the technique in question works for all fixed points except super attracting.

Well aware of that Daniel. That's not Kneser. That's just Schroder iteration about a fixed point. Kneser is far more involved. You are not solving a theta mapping...
Reply


Messages In This Thread
RE: Formula for the Talor Series for Tetration - by JmsNxn - 06/12/2022, 07:32 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 58,584 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Discussion on "tetra-eta-series" (2007) in MO Gottfried 40 42,410 02/22/2023, 08:58 PM
Last Post: tommy1729
  f(x+y) g(f(x)f(y)) = f(x) + f(y) addition formula ? tommy1729 1 3,180 01/13/2023, 08:45 PM
Last Post: tommy1729
Question Tetration Asymptotic Series Catullus 18 22,787 07/05/2022, 01:29 AM
Last Post: JmsNxn
  Calculating the residues of \(\beta\); Laurent series; and Mittag-Leffler JmsNxn 0 3,781 10/29/2021, 11:44 PM
Last Post: JmsNxn
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 3,622 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Reducing beta tetration to an asymptotic series, and a pull back JmsNxn 2 6,960 07/22/2021, 03:37 AM
Last Post: JmsNxn
  There is a non recursive formula for T(x,k)? marraco 5 12,033 12/26/2020, 11:05 AM
Last Post: Gottfried
  Perhaps a new series for log^0.5(x) Gottfried 3 10,842 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 40,265 02/20/2018, 09:55 PM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)