Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Moving between Abel's and Schroeder's Functional Equations
#1
Check out Moving between Abel's and Schroeder's Functional Equations
Reply
#2
(01/07/2020, 03:55 PM)Daniel Wrote: Check out Moving between Abel's and Schroeder's Functional Equations

Hey Daniel,

what if
Then Schroeder's equation , but is complex.  
Personally I think I prefer instead of for the complex valued Abel function.
There is a pair of complex valued Abel functions for the two complex conjugate fixed points, and there is a singularity at

Anyway, Kneser's tetration uses a Riemann mapping of , wrapping the real axis around a unit circle to eventually get to 
where there are two 1-cyclic theta(z) functions
 
where k is a constant as Im(z) gets arbitrarily large, and Kneser's slog or the inverse of Tetration would be

tau^{-1}(z) is also a z+1-cyclic function used to generate Tet(z) from the inverse of the complex valued Abel function.

https://math.eretrandre.org/tetrationfor...hp?tid=213
https://math.stackexchange.com/questions...55#2308955
- Sheldon
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  The Tao of Abel and Schroeder Daniel 0 142 12/24/2019, 11:25 AM
Last Post: Daniel
  Functional power Xorter 0 1,363 03/11/2017, 10:22 AM
Last Post: Xorter
  Taylor polynomial. System of equations for the coefficients. marraco 17 16,881 08/23/2016, 11:25 AM
Last Post: Gottfried
  Totient equations tommy1729 0 1,804 05/08/2015, 11:20 PM
Last Post: tommy1729
  Conservation of functional equation ? tommy1729 0 1,723 05/01/2015, 10:03 PM
Last Post: tommy1729
  Bundle equations for bases > 2 tommy1729 0 1,836 04/18/2015, 12:24 PM
Last Post: tommy1729
  Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 2,102 01/03/2015, 11:02 PM
Last Post: MphLee
  A system of functional equations for slog(x) ? tommy1729 3 4,523 07/28/2014, 09:16 PM
Last Post: tommy1729
  [stuck] On the functional equation of the slog : slog(e^z) = slog(z)+1 tommy1729 1 2,518 04/28/2014, 09:23 PM
Last Post: tommy1729
  functional type shifting patterns MikeSmith 0 2,170 09/30/2013, 03:25 AM
Last Post: MikeSmith



Users browsing this thread: 1 Guest(s)