Solving tetration for base 0 < b

Linear Mode

Solving tetration for base 0 < b < e^-e

mike3

Long Time Fellow

Posts: 368
Threads: 44
Joined: Sep 2009

#10

09/12/2009, 09:04 PM (This post was last modified: 09/12/2009, 09:05 PM by mike3.)

So then since neither of those worked, it seems all we're left with is the Ansus formula and the Cauchy integral (but determining the correct contours and asymptotic behavior, now that's the rub...).

I'm also curious: What about \( b = e^{-e} \) exactly? You said it converges slowly, but how do you iterate it at all? What is the asymptotic as the tower \( x \rightarrow \infty \)?

Find

« Next Oldest | Next Newest »

Messages In This Thread

Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 02:00 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 06:56 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:20 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 07:40 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:47 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:07 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 08:35 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:50 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 03:48 PM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 09:04 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 06:14 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 07:24 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 11:23 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 11:44 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/14/2009, 09:43 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/17/2009, 08:01 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/17/2009, 11:03 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 01:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 07:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/14/2009, 02:02 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 09:49 AM

RE: Solving tetration for base 0 < b < e^-e - by tommy1729 - 09/18/2009, 12:16 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/18/2009, 01:00 PM

Possibly Related Threads…
Thread		Author	Replies	Views	Last Post
	Kneser tetration Polynomial approximation for base e	RaeesHarris	0	1,029	09/02/2026, 07:59 PM Last Post: RaeesHarris
	Mixed-base tetration: five preprints, a faster fatou.gp fork, and a base-change calcu	Lightrunner	0	1,527	07/15/2026, 08:33 AM Last Post: Lightrunner
	Seeking an arXiv endorser for mixed-base tetration (math.DS)	Lightrunner	0	1,047	07/13/2026, 10:19 PM Last Post: Lightrunner
	Base -1	marraco	15	45,010	07/06/2022, 09:37 AM Last Post: Catullus
	I thought I'd take a crack at base = 1/2	JmsNxn	9	18,315	06/20/2022, 08:28 AM Last Post: Catullus
	solving f(g(x)) = f(x) converging to f(exp(x)) = f(x)	tommy1729	2	5,709	05/26/2022, 11:07 PM Last Post: JmsNxn
	Repetition of the last digits of a tetration of generic base	Luknik	12	26,174	12/16/2021, 12:26 AM Last Post: marcokrt
	On the [tex]2 \pi i[/tex]-periodic solution to tetration, base e	JmsNxn	0	4,434	09/28/2021, 05:44 AM Last Post: JmsNxn
	Complex Tetration, to base exp(1/e)	Ember Edison	7	27,721	08/14/2019, 09:15 AM Last Post: sheldonison
	b^b^x with base 0<b<e^-e have three real fixpoints	Gottfried	1	10,598	11/07/2017, 11:06 AM Last Post: sheldonison

View a Printable Version

Users browsing this thread: 2 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me