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 Iterated Hyperbolic Sine and Iterated Natural Logarithm Catullus Fellow Posts: 205 Threads: 46 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? ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Please remember to stay hydrated. Sincerely: Catullus JmsNxn Ultimate Fellow Posts: 940 Threads: 112 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: 1,676 Threads: 368 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 »

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