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 Regular "pentation"? andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 05/07/2010, 03:17 AM (05/01/2010, 11:56 AM)mike3 Wrote: It would be interesting to determine what the upper bound of the regular interval for the bases of pentation would be. We know that for tetration it is $e^{1/e}$, but what about pentation? (I suppose this would require tetration for b greater than $e^{1/e}$ to investigate, though, so we'd need other methods like the Abel iteration or the continuum sum (I'm a big fan of continuum sums, by the way )) I think I finally understand what you're talking about here. There is an interval that plays the same role in pentation as $(e^{-e}, e^{1/e})$ plays in tetration. I talked about the upper bound of this interval here, but whether or not there is a lower bound to this interval is unknown. Just as the point $(x=e^{1/e}, y=e)$ is the "highest" point on the graph of $y = x {\uparrow}{\uparrow} \infty$, so is $(x=1.6353, y=3.0885)$ the "highest" point on the graph of $y = x {\uparrow}{\uparrow}{\uparrow} \infty$. « 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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