Iterated Hyperbolic Sine and Iterated Natural Logarithm Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022   06/11/2022, 05:26 AM (This post was last modified: 08/14/2022, 09:19 PM by Catullus.) 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. ) 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\ JmsNxn Ultimate Fellow Posts: 1,178 Threads: 123 Joined: Dec 2010 06/11/2022, 07:37 AM (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!  TOMMY's METHOD! tommy1729 Ultimate Fellow Posts: 1,859 Threads: 402 Joined: Feb 2009 06/11/2022, 11:58 AM (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!  TOMMY's METHOD! yes ! https://math.eretrandre.org/tetrationfor...hp?tid=424 ( mainly ) regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post [MSE]root expressions and sine tommy1729 2 100 03/03/2023, 05:52 PM Last Post: tommy1729 [MSE] iterated sin using Besselfunction 1st kind Gottfried 7 573 12/18/2022, 02:06 PM Last Post: Gottfried Iterated function convergence Daniel 1 246 12/18/2022, 01:40 AM Last Post: JmsNxn Uniqueness of fractionally iterated functions Daniel 7 1,227 07/05/2022, 01:21 AM Last Post: JmsNxn Derivative of the Tetration Logarithm Catullus 1 560 07/03/2022, 07:23 AM Last Post: JmsNxn Natural Properties of the Tetra-Euler Number Catullus 6 1,063 07/01/2022, 08:16 AM Last Post: Catullus Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 14,255 05/26/2021, 11:55 PM Last Post: MphLee Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 4,055 09/09/2019, 10:50 PM Last Post: tommy1729 Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 18,529 08/07/2019, 02:44 AM Last Post: Ember Edison Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 19,401 06/10/2019, 04:29 AM Last Post: Ember Edison

Users browsing this thread: 1 Guest(s)