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 Change of base formula for Tetration sheldonison Long Time Fellow Posts: 633 Threads: 22 Joined: Oct 2008 05/05/2009, 11:21 AM (05/03/2009, 10:20 PM)tommy1729 Wrote: ??? how does change of base formula for tetration and exp(z) -1 relate ??? i would recommend -- in case this is important and proved -- that more attention is given to it on the forum and/or FAQI agree that the base conversion problem is very interesting, and needs more attention. Here's another way to write the change of base equation, converting from base a to base b. $\text{sexp}_b(x) = \text{ } \lim_{n \to \infty} \text{log}_b^{\circ n}(\text{sexp}_a (x + \text{slog}_a(\text{sexp}_b(n)))$ In this equation, $\text{slog}_a(\text{sexp}_b(n)))$ converges to n plus the base conversion constant. This base conversion will have a small 1-cyclic periodic wobble, $\theta(x)$, when compared to Dimitrii's solution. $\text{sexp}_b(x+\theta(x)) = \text{ } \lim_{n \to \infty} \text{log}_b^{\circ n}(\text{sexp}_a (x + \text{slog}_a(\text{sexp}_b(n)))$ Convergence for real values of x is easy to show, and emperically the derivatives appear continuous, but behavior for complex values is a more difficult problem. I would also like to characterize the $\theta(x)$ sinusoid, and find out whether or not it is c-oo, and whether the sexp_b(z) shows the singularities in the complex plane predicted by Dimitrii Kouznetsov. My thoughts started before I read Jay's post, but you can see them here, http://math.eretrandre.org/tetrationforu...hp?tid=236. « Next Oldest | Next Newest »

 Messages In This Thread Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:39 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 06:41 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:38 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 08:53 AM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 04:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/12/2007, 06:39 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:00 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:09 PM RE: Change of base formula for Tetration - by jaydfox - 08/12/2007, 09:30 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:47 PM RE: Change of base formula for Tetration - by andydude - 08/13/2007, 02:58 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 06:34 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:31 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 07:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:03 PM RE: Change of base formula for Tetration - by bo198214 - 08/13/2007, 08:23 PM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 08:32 PM RE: Change of base formula for Tetration - by bo198214 - 08/15/2007, 09:36 AM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 10:15 AM RE: Change of base formula for Tetration - by jaydfox - 08/13/2007, 03:42 PM RE: Change of base formula for Tetration - by jaydfox - 08/15/2007, 11:29 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:21 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:32 PM RE: Change of base formula for Tetration - by jaydfox - 08/16/2007, 09:49 PM RE: Change of base formula for Tetration - by bo198214 - 08/16/2007, 09:53 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 03:51 AM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 06:24 AM RE: Change of base formula for Tetration - by bo198214 - 08/31/2007, 09:03 AM RE: Change of base formula for Tetration - by tommy1729 - 05/03/2009, 10:20 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 11:21 AM RE: Change of base formula for Tetration - by tommy1729 - 05/05/2009, 12:19 PM RE: Change of base formula for Tetration - by sheldonison - 05/05/2009, 01:29 PM RE: Change of base formula for Tetration - by bo198214 - 05/05/2009, 01:37 PM RE: Change of base formula for Tetration - by jaydfox - 08/31/2007, 04:11 AM Convergence of Jay's change of base formula - by bo198214 - 08/15/2007, 09:00 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 09:19 PM RE: Parabolic Iteration - by bo198214 - 08/15/2007, 09:30 PM RE: Parabolic Iteration - by jaydfox - 08/15/2007, 11:41 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 08:17 AM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 05:51 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 06:40 PM RE: Parabolic Iteration - by jaydfox - 08/16/2007, 09:47 PM RE: Parabolic Iteration - by bo198214 - 08/16/2007, 10:07 PM

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