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 Comparing the Known Tetration Solutions andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/22/2007, 11:28 PM Well, I've prepared some graphs in the hope that I can address the question about my super-logarithm extension. The question was "are you sure?" about my super-logarithm definition not working for bases between $1. My only answer is to look at the graphs. These are some graphs of the first three coefficients of the super-logarithm, i.e. the Abel function of $b^x$. In each graph there are multiple curves, each curve corresponds to a specific approximation; the approximations shown are roughly $n=\{2, 3, 4, ..., 10\}$ and the independant axis represents the base $1 < b < 4$. What follows are graphs of $A_k$ as functions of b for $k=\{1, 2, 3\}$ for the functional equation $A(b^x) = A(x) +1$ with $A(0) = -1$. As you can see, when the base is between $1, although the matrix equation has a solution, the solutions (coefficients) do not seem to converge. This is what leads me to beleive that my super-logarithm definition will only work for $b>\eta$. 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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