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 Comparing the Known Tetration Solutions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/18/2007, 11:59 AM (This post was last modified: 08/18/2007, 11:59 AM by bo198214.) andydude Wrote:I just wanted to clarify that my super-logarithm solution only works for $x > e^{1/e}$ even though my pdf says $x > 1$. I think that the reason for this is that tetration for bases between 1 and $e^{1/e}$ has an upper limit (due to the convergence of ${}^{\infty}x$), and thus the super-logarithm has a limited domain over which it is defined.Are you sure, what goes wrong for bases $b<\eta$? I mean it is clear that the domain of the superlog is bounded above by the lower fixed point of $b^x=x$, which I will call $\beta(b)$ and which is $\beta(b)=W(-\log(b))/(-\log(b))$. So $\text{slog}_b(x)$ is allowed only for $x<\beta(b)$ because $\lim_{n\to\infty}{}^nb=\beta(b)$. What goes wrong for those arguments with your superlog? « 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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