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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?
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ
Please remember to stay hydrated.
Sincerely: Catullus
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#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!
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#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
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