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Base -1
Catullus Offline
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#10
06/19/2022, 11:01 PM (This post was last modified: 07/06/2022, 08:09 AM by Catullus.)
(05/22/2015, 05:28 AM)sheldonison Wrote:
(05/21/2015, 06:31 PM)marraco Wrote: Tetration base 1 is a constant function equal to 1, for x>-1, and has a discontinuity at -1. Or at least that's the solution if \( \\[15pt]

{^{x}1=\lim_{b \to 1} ^xb} \)... I wonder if there is a family of continuous solutions, and this one is the evolvent.

b=-1 has two primary fixed points. both repelling; I'm not sure what the other fixed points are. 
-1,
0.266036599292773 + 0.294290021873387*I
They can be calculated with the Lambert W function, as [Image: svg.image?LambertW(-i\pi)*i\div\pi\foral...\mathbb%7BZ%7D].
Please remember to stay hydrated.
ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
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Messages In This Thread
Base -1 - by marraco - 05/21/2015, 06:31 PM
RE: Base -1 - by sheldonison - 05/22/2015, 05:28 AM
RE: Base -1 - by Catullus - 06/19/2022, 11:01 PM
RE: Base -1 - by sheldonison - 06/01/2015, 03:46 AM
RE: Base -1 - by marraco - 06/02/2015, 01:08 PM
RE: Base -1 - by sheldonison - 06/02/2015, 05:27 PM
RE: Base -1 - by Daniel - 06/19/2022, 11:34 PM
RE: Base -1 - by JmsNxn - 06/20/2022, 12:40 AM
RE: Base -1 - by Daniel - 06/20/2022, 01:01 AM
RE: Base -1 - by Daniel - 06/20/2022, 03:21 AM
RE: Base -1 - by JmsNxn - 06/20/2022, 02:37 AM
RE: Base -1 - by Catullus - 07/06/2022, 09:37 AM

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