Login

tommy1729 · 03/07/2013, 12:16 AM

Is the half iterate of 2sinh(x) - expanded from fixpoint 0 - analytic near R ?
And does it satisfy its functional equation ( composition towards 2sinh(x) ) wherever it is analytic ( near R ) ?

I know the taylor series is messed up because we have 2 complex conjugate fixpoints.

However a taylor series can converge outside its radius.

This might be a general idea that we need a general tool for.

regards

tommy1729

tommy1729 · 03/13/2013, 12:13 AM

Does the taylor series expanded from 0 converge outside its radius ?

Login
Username:
Password:	Lost Password?
	Remember me

Possibly Related Threads...
Thread		Author	Replies	Views	Last Post
	Half-iterates and periodic stuff , my mod method [2019]	tommy1729	0	238	09/09/2019, 10:55 PM Last Post: tommy1729
	Approximation to half-iterate by high indexed natural iterates (base on ShlThrb)	Gottfried	1	402	09/09/2019, 10:50 PM Last Post: tommy1729
	[repost] A nowhere analytic infinite sum for tetration.	tommy1729	0	1,078	03/20/2018, 12:16 AM Last Post: tommy1729
	Analytic matrices and the base units	Xorter	2	2,268	07/19/2017, 10:34 AM Last Post: Xorter
	Does tetration take the right half plane to itself?	JmsNxn	7	5,707	05/16/2017, 08:46 PM Last Post: JmsNxn
	Non-analytic	Xorter	0	1,346	04/04/2017, 10:38 PM Last Post: Xorter
	Half-iteration of x^(n^2) + 1	tommy1729	3	3,856	03/09/2017, 10:02 PM Last Post: Xorter
	A conjectured uniqueness criteria for analytic tetration	Vladimir Reshetnikov	13	10,587	02/17/2017, 05:21 AM Last Post: JmsNxn
	tommy's simple solution ln^[n](2sinh^[n+x](z))	tommy1729	1	2,372	01/17/2017, 07:21 AM Last Post: sheldonison
	Uniqueness of half-iterate of exp(x) ?	tommy1729	14	14,309	01/09/2017, 02:41 AM Last Post: Gottfried