Half-iterate exp(z)-1: hypothese on growth of coefficients

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Half-iterate exp(z)-1: hypothese on growth of coefficients

Gottfried Offline

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#35

08/18/2022, 07:44 PM (This post was last modified: 08/18/2022, 08:26 PM by Gottfried.)

(08/18/2022, 07:05 PM)bo198214 Wrote: Interestingly the iterative logarithm of \(e^x-1\) follows a similar pattern.
(...)
with the advantage that it doesn't depend on t, which we took as t=1/2.

Wow. This makes me happy to see :-) !
Now the question comes up, why, for fractional multiplier \( h \) the exponential of the logit() keeps this form while for integer \( h \) the sinusoidal effect disappears and the known -entire- exponentail series comes to light... Hmmm. well, in my other picture we see, that the index \( \kappa \) "from where divergence begins", goes to infinity as the fractional part of \( h \) goes to zero... Perhaps we're going to find "the key"...

Gottfried Helms, Kassel

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Messages In This Thread

Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/19/2022, 08:11 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/19/2022, 09:40 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/19/2022, 10:19 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/21/2022, 12:15 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/21/2022, 01:13 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/21/2022, 02:18 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/20/2022, 10:49 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/21/2022, 07:30 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/22/2022, 01:44 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/22/2022, 02:57 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/24/2022, 02:23 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/06/2022, 09:56 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/07/2022, 09:19 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/06/2022, 10:14 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/07/2022, 09:51 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/10/2022, 02:12 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/11/2022, 03:28 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/11/2022, 07:03 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/11/2022, 01:26 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/12/2022, 01:47 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/15/2022, 05:24 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/18/2022, 04:48 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/18/2022, 11:37 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 06:25 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 04:36 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/19/2022, 06:26 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/28/2022, 01:41 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/28/2022, 03:45 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/29/2022, 05:05 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 08:01 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/18/2022, 12:17 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 07:05 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/18/2022, 07:44 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 05:12 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 05:24 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 05:35 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 05:54 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 06:17 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 06:54 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 07:05 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 07:57 AM

RE: Parabolic Formal Powerseries - by tommy1729 - 09/09/2022, 12:24 AM

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