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Tetration below 1
#7
The interval b in (0, 1) is a very difficult region to do tetration over. The best that I have been able to do is something similar to my matrix equations, only instead of being automated, I solve each step of the way manually. From my manual solutions (i.e. using a 4-th degree polynomial, changing coefficients as necessary) I have found that tetration over the critical interval (-1<x<0) can be approximated by where 0<b<1 and -1<x<0, is much more sinusoidal than with higher bases (where usually for example). One of the reasons is that for b>1 and for b<1. In order for the curve to get the "direction" in needs to go in, it needs to be more sinusoidal, than linear as with b=e.

For more about the domain and the line where x=-2, see my previous post
http://math.eretrandre.org/tetrationforu...287#pid287
about the domain of real-valued (and possibly real-analytic) tetraiton.

Andrew Robbins
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Messages In This Thread
Tetration below 1 - by bo198214 - 08/29/2007, 06:14 PM
RE: Tetration below 1 - by Daniel - 08/30/2007, 09:32 PM
RE: Tetration below 1 - by jaydfox - 08/30/2007, 11:08 PM
RE: Tetration below 1 - by jaydfox - 08/30/2007, 11:20 PM
RE: Tetration below 1 - by Daniel - 08/31/2007, 12:47 AM
RE: Tetration below 1 - by GFR - 09/02/2007, 01:30 PM
RE: Tetration below 1 - by bo198214 - 09/02/2007, 01:40 PM
RE: Tetration below 1 - by GFR - 09/02/2007, 05:38 PM
RE: Tetration below 1 - by jaydfox - 09/03/2007, 03:58 PM
RE: Tetration below 1 - by bo198214 - 09/03/2007, 04:07 PM
RE: Tetration below 1 - by jaydfox - 09/03/2007, 04:36 PM
RE: Tetration below 1 - by jaydfox - 09/05/2007, 11:24 PM
RE: Tetration below 1 - by GFR - 09/06/2007, 12:01 AM
RE: Tetration below 1 - by jaydfox - 09/06/2007, 03:28 AM
RE: Tetration below 1 - by jaydfox - 09/06/2007, 07:21 AM
RE: Tetration below 1 - by bo198214 - 03/26/2008, 04:51 PM



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