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
  [MSE] iterated sin using Besselfunction 1st kind Gottfried 7 443 12/18/2022, 02:06 PM
Last Post: Gottfried
  Iterated function convergence Daniel 1 184 12/18/2022, 01:40 AM
Last Post: JmsNxn
  Uniqueness of fractionally iterated functions Daniel 7 1,078 07/05/2022, 01:21 AM
Last Post: JmsNxn
Question Derivative of the Tetration Logarithm Catullus 1 506 07/03/2022, 07:23 AM
Last Post: JmsNxn
Question Natural Properties of the Tetra-Euler Number Catullus 6 942 07/01/2022, 08:16 AM
Last Post: Catullus
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 13,833 05/26/2021, 11:55 PM
Last Post: MphLee
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 3,985 09/09/2019, 10:50 PM
Last Post: tommy1729
  Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 18,188 08/07/2019, 02:44 AM
Last Post: Ember Edison
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 19,079 06/10/2019, 04:29 AM
Last Post: Ember Edison
  iterated derivation Xorter 0 2,667 06/09/2019, 09:43 PM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)