Tetration Forum › Tetration and Related Topics › Mathematical and General Discussion v
solving f(g(x)) = f(x) converging to f(exp(x)) = f(x)

Linear Mode
solving f(g(x)) = f(x) converging to f(exp(x)) = f(x)
JmsNxn Offline
Ultimate Fellow
*****
Posts: 1,214
Threads: 126
Joined: Dec 2010
#3
05/26/2022, 11:07 PM (This post was last modified: 05/26/2022, 11:08 PM by JmsNxn.)
Guess I never saw this thread.

I absolutely believe this will converge pointwise at least. But can we be sure that the Taylor series is convergent?

Sounds like Andrew's slog, but I like this more, seems more tangible.

I do not think it'll be easy to show the radius of convergence is non zero though. And we need it to be \(|L|\). Sounds really hard to be honest.
Find
Reply


Messages In This Thread
RE: solving f(g(x)) = f(x) converging to f(exp(x)) = f(x) - by JmsNxn - 05/26/2022, 11:07 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 3,553 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Solving tetration using differintegrals and super-roots JmsNxn 0 6,504 08/22/2016, 10:07 PM
Last Post: JmsNxn
  Solving tetration for base 0 < b < e^-e mike3 24 77,499 09/18/2009, 01:00 PM
Last Post: bo198214
  Naturally solving the sexp bo198214 2 14,042 08/22/2007, 08:58 AM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)