Iterated Hyperbolic Sine and Iterated Natural Logarithm
#1
Question 
If you do ln(sinh(x)) and ln(ln(sinh(sinh(x)))) and ln(ln(ln(sinh(sinh(sinh(x)))))) they do seem to converge.
Also if you iterate 2sinh instead of sinh it also seems to converge. (I like the 2sinh function a lot by the way. Tongue)
Does anyone know of any closed forms of what these converge to?
Please remember to stay hydrated.
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
Reply
#2
(06/11/2022, 05:26 AM)Catullus Wrote: If you do ln(sinh(x)) and ln(ln(sinh(sinh(x)))) and ln(ln(ln(sinh(sinh(sinh(x)))))) they do seem to converge.
Also if you iterate 2sinh instead of sinh it also seems to converge.
Does anyone know of any closed forms of what these converge to?
Also his is my 64th post!  Smile

TOMMY's METHOD!
Reply
#3
(06/11/2022, 07:37 AM)JmsNxn Wrote:
(06/11/2022, 05:26 AM)Catullus Wrote: If you do ln(sinh(x)) and ln(ln(sinh(sinh(x)))) and ln(ln(ln(sinh(sinh(sinh(x)))))) they do seem to converge.
Also if you iterate 2sinh instead of sinh it also seems to converge.
Does anyone know of any closed forms of what these converge to?
Also his is my 64th post!  Smile

TOMMY's METHOD!

yes !

https://math.eretrandre.org/tetrationfor...hp?tid=424

( mainly )

regards

tommy1729
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  4 hypothesis about iterated functions Shanghai46 11 13,007 04/22/2023, 08:22 PM
Last Post: Shanghai46
  Question about the properties of iterated functions Shanghai46 9 11,362 04/21/2023, 09:07 PM
Last Post: Shanghai46
  [MSE]root expressions and sine tommy1729 2 3,263 03/03/2023, 05:52 PM
Last Post: tommy1729
  [MSE] iterated sin using Besselfunction 1st kind Gottfried 7 8,776 12/18/2022, 02:06 PM
Last Post: Gottfried
  Iterated function convergence Daniel 1 4,058 12/18/2022, 01:40 AM
Last Post: JmsNxn
  Uniqueness of fractionally iterated functions Daniel 7 11,005 07/05/2022, 01:21 AM
Last Post: JmsNxn
Question Derivative of the Tetration Logarithm Catullus 1 3,244 07/03/2022, 07:23 AM
Last Post: JmsNxn
Question Natural Properties of the Tetra-Euler Number Catullus 6 10,051 07/01/2022, 08:16 AM
Last Post: Catullus
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 43,236 05/26/2021, 11:55 PM
Last Post: MphLee
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 7,581 09/09/2019, 10:50 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)