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 Regular "pentation"? mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 05/02/2010, 12:07 AM (This post was last modified: 05/02/2010, 12:09 AM by mike3.) Actually, I already saw some of those posts. I'm not sure if the use of regular iteration at the lower (repelling) fixed point would be the best choice for pentation of bases greater than the constant where the pentation goes off toward infinity, just as we don't use the lower fixed point of exponential to build the tetration at $b > e^{1/e}$. The reason for this is that I think the result of the regular iteration at the upper and lower fixed point differs (doesn't it?) for $1 < b < K$, where $K$ is the constant beyond which $^{x} b$ no longer has an attracting fixed point and so $b \uparrow \uparrow \uparrow x \rightarrow \infty$ as $x \rightarrow \infty$. Instead, I'd think it'd make more sense to use the upper fixed point for $1 < b < K$, same as the case for the tetration, and then one needs more sophisticated methods like the Abel-matrix, matrix-power, or continuum-sum for bases beyond that constant $K$ (according to one post it's somewhat over 1.6). « Next Oldest | Next Newest »

 Messages In This Thread Regular "pentation"? - by mike3 - 05/01/2010, 11:56 AM RE: Regular "pentation"? - by tommy1729 - 05/01/2010, 03:21 PM RE: Regular "pentation"? - by bo198214 - 05/01/2010, 08:54 PM RE: Regular "pentation"? - by mike3 - 05/02/2010, 12:07 AM RE: Regular "pentation"? - by andydude - 05/02/2010, 09:12 AM RE: Regular "pentation"? - by Base-Acid Tetration - 05/02/2010, 11:29 PM RE: Regular "pentation"? - by andydude - 05/03/2010, 02:54 AM RE: Regular "pentation"? - by mike3 - 05/03/2010, 03:27 AM RE: Regular "pentation"? - by andydude - 05/07/2010, 03:10 AM RE: Regular "pentation"? - by andydude - 05/07/2010, 03:17 AM RE: Regular "pentation"? - by mike3 - 05/07/2010, 06:07 AM pentation? (Based on "polynomial" tetration) - by Gottfried - 03/29/2011, 09:50 AM RE: pentation? (Based on "polynomial" tetration) - by BenStandeven - 04/04/2011, 03:16 AM

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