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

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

andydude Offline

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#18

10/24/2009, 12:26 AM (This post was last modified: 10/24/2009, 12:27 AM by andydude.)

(10/23/2009, 09:27 PM)Base-Acid Tetration Wrote: Is it me, or will pentation indeed look a lot like tetration in the complex plane?

Well, if by "look like" you mean it will have 2 branchcuts (\( -1.6 \pm 1.33i \)) instead of 1 branchcut (-2), and 4 primary fixedpoints instead of 3 primary fixedpoints, then yes.

Below is a complex plot of \( \text{pexp}(z) - z \), and even though there is a bit of double-vision, it is clear that there are 4 fixedpoints near the origin.

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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

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