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 Comparing the Known Tetration Solutions andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/17/2007, 11:20 PM If by my solution you mean ${\ }^{y}(e^{1/e})$ through parabolic iteration of $e^x-1$ and by Daniel's you mean ${\ }^{y}(b^{1/b})$ through hyperbolic iteration of $b^x-1$, then yes, I'd be happy to provide some high-quality graphics and numerical tables. I still need to re-read Jay's solution, since it seems dependent on the super-logarithmic constant which I don't understand yet. Also you brought up an interesting point that may prevent comparison of all methods, since some methods work over non-overlapping intervals. Tetration can be divided into several intervals in terms of what values of x in ${}^{y}x$ are valid for that definition: the parabolic point $e^{1/e}$, the hyperbolic interval $(e^{-e}, e^{1/e})$, and I suppose would you could call the elliptic? interval $(e^{1/e}, \infty)$, which is what my definition of the super-logarithm is valid for. These are all closely tied to the interval of convergence of the infinite hyper-power ${}^{\infty}x$ which was found almost 230 years ago. My how time has passed... Andrew Robbins « Next Oldest | Next Newest »

 Messages In This Thread Comparing the Known Tetration Solutions - by bo198214 - 08/17/2007, 09:13 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/20/2007, 09:59 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/20/2007, 11:09 AM New pictures from the hyperbolic slog! - by bo198214 - 08/20/2007, 01:36 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/20/2007, 05:35 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/21/2007, 05:06 AM RE: Comparing the Known Tetration Solutions - by andydude - 08/22/2007, 11:28 PM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/23/2007, 12:14 AM RE: Comparing the Known Tetration Solutions - by Gottfried - 08/29/2007, 06:19 AM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 06:15 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 12:06 AM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 01:56 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/29/2007, 07:48 AM RE: Comparing the Known Tetration Solutions - by andydude - 08/29/2007, 08:19 AM RE: computing the iterated exp(x)-1 - by andydude - 08/17/2007, 11:20 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/17/2007, 11:38 PM RE: computing the iterated exp(x)-1 - by bo198214 - 08/17/2007, 11:45 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 12:19 AM RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 08:19 AM RE: computing the iterated exp(x)-1 - by andydude - 08/18/2007, 09:35 AM RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 11:59 AM RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 03:49 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/19/2007, 12:50 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/19/2007, 10:55 AM

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