Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation

Linear Mode

Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation

andydude Offline

Long Time Fellow

Posts: 510
Threads: 44
Joined: Aug 2007

#16

10/23/2009, 09:03 PM

I also remember someone asking about fixedpoints of tetration, so I graphed some complex plots of \( e^z - z \) and \( {}^{z}e - z \) for comparison.

It looks as though there are fixedpoints of tetration at:

\( z = -1.85 \)
\( z = 0.8 \pm 1.5 i \)
\( z = 3 \pm 0.5 i \)
and more...

Attached Files
.pdf

plot-expx-minus-x.pdf (Size: 443.39 KB / Downloads: 1,235)
.pdf

plot-sexpx-minus-x.pdf (Size: 428.64 KB / Downloads: 1,206)
.pdf

plot-sexpx-minus-x-big.pdf (Size: 447.15 KB / Downloads: 1,262)

Website Find

« Next Oldest | Next Newest »

Messages In This Thread

Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/13/2009, 03:53 AM

RE: complex fixed points of tetration/tetralogarithm - by bo198214 - 10/13/2009, 07:45 AM

RE: complex fixed points of tetration/tetralogarithm - by Base-Acid Tetration - 10/13/2009, 07:46 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/13/2009, 09:47 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/15/2009, 08:17 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/15/2009, 05:01 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/15/2009, 09:39 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/16/2009, 06:28 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/16/2009, 08:52 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/17/2009, 10:47 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by bo198214 - 10/17/2009, 04:37 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/17/2009, 08:23 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/17/2009, 02:59 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/17/2009, 09:29 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/23/2009, 08:01 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/23/2009, 09:03 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/23/2009, 09:27 PM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/24/2009, 12:26 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by Base-Acid Tetration - 10/24/2009, 12:31 AM

RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/24/2009, 04:12 AM

Possibly Related Threads…
Thread		Author	Replies	Views	Last Post
	Mixed-base tetration: five preprints, a faster fatou.gp fork, and a base-change calcu	Lightrunner	0	346	07/15/2026, 08:33 AM Last Post: Lightrunner
	Seeking an arXiv endorser for mixed-base tetration (math.DS)	Lightrunner	0	246	07/13/2026, 10:19 PM Last Post: Lightrunner
	Tetration with complex bases	TetrationSheep	0	1,318	11/13/2025, 10:33 AM Last Post: TetrationSheep
	Real tetration as a limit of complex tetration	Daniel	5	11,037	06/20/2023, 07:52 PM Last Post: tommy1729
	[2sinh] exp(x) - exp( - (e-1) x), Low Base Constant (LBC) 1.5056377..	tommy1729	3	6,773	04/30/2023, 01:22 AM Last Post: tommy1729
	Down with fixed points!	Daniel	1	3,285	04/29/2023, 11:02 PM Last Post: tommy1729
	Real and complex tetration	Daniel	13	20,192	04/04/2023, 10:25 AM Last Post: JmsNxn
	Evaluating Arithmetic Functions In The Complex Plane	Caleb	6	10,367	02/20/2023, 12:16 AM Last Post: tommy1729
	Iteration with two analytic fixed points	bo198214	62	84,949	11/27/2022, 06:53 AM Last Post: JmsNxn
	Range of complex tetration as real	Daniel	2	5,864	10/22/2022, 08:08 PM Last Post: Shanghai46

View a Printable Version

Users browsing this thread: 1 Guest(s)

Login
Username:
Password:	Lost Password?
	Remember me