Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
matrix function like iteration without power series expansion
#16
andydude Wrote:Awhile back, I did some test with parabolic iteration, and convinced myself that Woon's formula and Jabotinsky's formula produce exactly the same results for parabolic iteration (for symbolic coefficients). So I could write up something about this if needed.

The problematic thing about parabolic iteration is convergence. You usually only have an asymptotic development at the fixed point. I.e. the series is not developable at the fixed point however in every neighborhood and all the coefficients converge (towards the fixed point in a certain sector) to that of the asymptotic development.

I also see that I made mistake in my first post about the convergence of that series. It is not true that the series always converges if the function has a finite attracting fixed point.
Reply


Messages In This Thread
RE: matrix function like iteration without power series expansion - by bo198214 - 07/14/2008, 09:55 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 691 03/21/2020, 08:28 AM
Last Post: Daniel
  New mathematical object - hyperanalytic function arybnikov 4 1,043 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 662 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 3,784 02/18/2019, 10:34 PM
Last Post: Micah
  Degamma function Xorter 0 1,123 10/22/2018, 11:29 AM
Last Post: Xorter
Question Taylor series of i[x] Xorter 12 13,329 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,510 03/11/2017, 10:22 AM
Last Post: Xorter
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,832 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,884 12/21/2016, 01:27 PM
Last Post: tommy1729
  2 fixpoints related by power ? tommy1729 0 1,665 12/07/2016, 01:29 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)