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 Change of base formula for Tetration tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 05/05/2009, 12:19 PM (05/05/2009, 11:21 AM)sheldonison Wrote: (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. the problem is the wobble ... its a bit of an illusionary use : first you give a formula to compute sexp_b(x) bye using sexp_b(n) then you correct sexp_b(x) to sexp_b(x + wobble(x)) which basicly just means ; you got a formula for sexp_b(n) using sexp_b(n) ... ?!? thats pretty lame selfreference ... ( godel escher and bach anyone ? :p ) furthermore , i asked how change of base formula for tetration and exp(z) - 1 relate ? that isnt answered ... furthermore i had the idea that slog_a(x) - slog_b(x) =/= 0 for a =/= b =/= x and a,b,x > e^e and slog_a(x)' - slog_b(x)' =/= 0 for a =/= b =/= x and a,b,x > e^e ( derivative with respect to x ) and that this might require a different Coo slog but would imply a uniqueness condition ? also the equation lim slog_a(oo) - slog_b(oo) = x seems intresting. regards tommy1729 « 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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