A tiny base-dependent formula for tetration (change-of-base?)

Linear Mode

A tiny base-dependent formula for tetration (change-of-base?)

Gottfried Offline

Ultimate Fellow

Posts: 904
Threads: 131
Joined: Aug 2007

03/17/2009, 06:36 PM (This post was last modified: 12/30/2017, 09:20 PM by Gottfried.)

Hmm, curious... curious... ,

things evolve a bit more. From the tetrated pascalmatrices we can also derive a fractional iteration if we apply the binomial-formula to the sequence of powerseries for different heights. Since the powerseries have this stunning smooth behave for increasing heights, the binomially interpolated series are accordingly smooth.
This seems all to be too crazy.... very smooth for the convergence bases and possibly continuable for the divergent cases, don't see it yet.

See the new chapter 2 in
PascalmatrixTetrated

Gottfried

Gottfried Helms, Kassel

Website Find

« Next Oldest | Next Newest »

Messages In This Thread

A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/14/2009, 09:17 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Ivars - 03/15/2009, 08:50 AM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/16/2009, 03:20 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by sheldonison - 03/16/2009, 01:36 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/16/2009, 02:59 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by sheldonison - 03/16/2009, 11:01 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/17/2009, 12:12 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/17/2009, 06:36 PM

RE: A tiny base-dependent formula for tetration (change-of-base?) - by Gottfried - 03/18/2009, 07:26 PM

Possibly Related Threads…
Thread		Author	Replies	Views	Last Post
	[2sinh] exp(x) - exp( - (e-1) x), Low Base Constant (LBC) 1.5056377..	tommy1729	3	6,471	04/30/2023, 01:22 AM Last Post: tommy1729
	f(x+y) g(f(x)f(y)) = f(x) + f(y) addition formula ?	tommy1729	1	3,564	01/13/2023, 08:45 PM Last Post: tommy1729
	Base -1	marraco	15	39,498	07/06/2022, 09:37 AM Last Post: Catullus
	I thought I'd take a crack at base = 1/2	JmsNxn	9	15,266	06/20/2022, 08:28 AM Last Post: Catullus
	Formula for the Taylor Series for Tetration	Catullus	8	15,042	06/12/2022, 07:32 AM Last Post: JmsNxn
	Repetition of the last digits of a tetration of generic base	Luknik	12	21,874	12/16/2021, 12:26 AM Last Post: marcokrt
	On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e	JmsNxn	0	3,797	09/28/2021, 05:44 AM Last Post: JmsNxn
	A different approach to the base-change method	JmsNxn	0	4,186	03/17/2021, 11:15 PM Last Post: JmsNxn
	There is a non recursive formula for T(x,k)?	marraco	5	12,991	12/26/2020, 11:05 AM Last Post: Gottfried
	[MSE] Shape of orbit of iterations with base b on Shell-Thron-region	Gottfried	14	44,010	12/13/2019, 02:33 PM Last Post: Ember Edison

View a Printable Version

Users browsing this thread: 1 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me