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 Comparing the Known Tetration Solutions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/17/2007, 11:45 PM (This post was last modified: 08/17/2007, 11:48 PM by bo198214.) andydude Wrote:If by my solution you mean ${\ }^{y}(e^{1/e})$ through parabolic iteration of $e^x-1$No, I meant the piecewise infinite differentiable definition of slog. Isnt it defined for arbirtrary bases? (I think you wrote for base greater 1.) So if you have the slog you have also the "sexp". And I would compare this with what comes out from Daniel's solution for the hyperbolic case (there is then no problem with the convergence radius of the series). Quote:and by Daniel's you mean ${\ }^{y}(b^{1/b})$ through hyperbolic iteration of $b^x-1$ Rather $b^x-x_0$, i.e. to develop $b^x$ at the (lower) fixed point $b^{x_0}=x_0$ which is given (if I remember correctly) by $x_0=\frac{W(-\log(b))}{-\log(b)}$ and then take hyperbolic iterations ${}^xb=\exp^{\circ x}_b(1.0)$. « 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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