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 tetration base conversion, and sexp/slog limit equations sheldonison Long Time Fellow Posts: 630 Threads: 22 Joined: Oct 2008 02/20/2009, 02:51 PM (This post was last modified: 02/20/2009, 05:15 PM by sheldonison.) bo198214 Wrote:But this question is different from whether $\text{slog}_a(x)-\text{slog}_b(x)$ converges to a constant, if we assume $a,b>e^{1/e}$. If $\text{slog}_a(x)-\text{slog}_b(x)$ does converge for $x\to\infty$ then - as $\text{sexp}_b$ goes to infinity - also $\text{slog}_a(\text{sexp}_b(x))-x$ converges. But this means that $\text{slog}_a(\text{sexp}_b(x))$ can not converge to a constant and vice versa. typo: $\text{slog}_a(\text{sexp}_b(x))-x$ is what converges to a cyclic 1-cycle function as x grows larger and may converge to a constant as x grows larger for some definitions of slog/sexp. Quote:But it never gets completely linear, doesnt it? Otherwise it would not be analytic. no, of course not. But I think the contributions of the higher order terms versus a linear estimate between the second and third terms, or between $\text{log}_b(e)$ and $\text{log}_b(\text{log}_b(e))$, becomes insignificant. I plan to try and show that the second and higher order derivatives for the two points, contribute an insignificant delta as b approaches $e^{1/e}$, and that in the limit, the linear term dominates the higher order terms by an arbitrarily large amount, and that the linear approximation suffices as a definition for the tetration for base b. I had originally intended this thread to be a search for other links about about base changes for tetration. I seem to have gotten side tracked on to defining the sexp function for real numbers for bases $>e^{1/e}$. - Sheldon Levenstein « Next Oldest | Next Newest »

 Messages In This Thread tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/18/2009, 07:01 AM RE: tetration base conversion, questions and results - by sheldonison - 02/19/2009, 12:10 AM tetration base conversion, uniqueness criterion? - by bo198214 - 02/19/2009, 04:24 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/20/2009, 10:54 AM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/20/2009, 01:07 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/20/2009, 02:51 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/21/2009, 12:18 AM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/21/2009, 12:39 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/21/2009, 02:59 PM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/21/2009, 06:36 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/22/2009, 04:41 AM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/22/2009, 04:04 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/24/2009, 08:24 PM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/24/2009, 09:57 PM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/24/2009, 10:21 PM RE: tetration base conversion, uniqueness criterion? - by sheldonison - 02/24/2009, 10:54 PM RE: tetration base conversion, uniqueness criterion? - by bo198214 - 02/24/2009, 11:06 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/26/2009, 11:04 AM RE: tetration base conversion, and sexp/slog limit equations - by bo198214 - 02/26/2009, 12:16 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/26/2009, 02:36 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/28/2009, 05:56 AM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/28/2009, 10:01 AM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 03/01/2009, 12:18 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 03/03/2009, 06:15 PM RE: tetration base conversion, and sexp/slog limit equations - by bo198214 - 03/03/2009, 06:46 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 03/03/2009, 07:27 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 03/09/2009, 06:34 PM Summay tetration base conversion, and sexp/slog limit equations - by sheldonison - 07/31/2009, 06:55 PM RE: Summay tetration base conversion, and sexp/slog limit equations - by sheldonison - 08/01/2009, 10:32 AM Is it analytic? - by sheldonison - 12/22/2009, 11:39 PM RE: tetration base conversion, and sexp/slog limit equations - by mike3 - 12/25/2009, 08:51 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 12/26/2009, 01:44 AM RE: tetration base conversion, and sexp/slog limit equations - by mike3 - 12/26/2009, 01:54 AM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 12/27/2009, 06:53 AM RE: tetration base conversion, and sexp/slog limit equations - by mike3 - 12/31/2009, 11:45 PM Inherent ringing in tetration, re: base conversion - by sheldonison - 01/02/2010, 05:31 AM RE: Inherent ringing in tetration, base conversion - by mike3 - 01/04/2010, 03:51 AM RE: Inherent ringing in tetration, base conversion - by sheldonison - 01/04/2010, 06:08 AM RE: tetration base conversion, and sexp/slog limit equations - by tommy1729 - 02/26/2013, 10:47 PM RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/27/2013, 07:05 PM

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