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 Change of base formula for Tetration sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 05/05/2009, 01:29 PM (This post was last modified: 05/05/2009, 03:04 PM by sheldonison.) (05/03/2009, 10:20 PM)tommy1729 Wrote: 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 )Well, its not that bad, since n is an integer, sexp_b(n) is well defined. You can leave off the $\theta(x)$ function, you just get a different solution, one that wobbles a little bit, easier to see in the higher derivatives. Also, in my original post, I was using a home base of $\eta+\delta$ where $\eta=e^{1/e}$, whose sexp solution I was able to derive, see http://math.eretrandre.org/tetrationforu...236&page=1. (05/03/2009, 10:20 PM)tommy1729 Wrote: furthermore , i asked how change of base formula for tetration and exp(z) - 1 relate ? that isnt answered ...Jay isn't around to answer. He discusses base change convergence, which I understand perfectly well. But I didn't understand the double logarithmic paragraph. Jay abandoned this approach to tetration, because it gives different results than Andrew Robbin's solution, (and Dimitrii Kouznetsov's solution) due to the wobble. (05/03/2009, 10:20 PM)tommy1729 Wrote: furthermore i had the idea that slog_a(x) - slog_b(x) =/= 0 for a =/= b =/= x and a,b,x > e^e For large enough values of x, slog_a(x) - slog_b(x) will converge to a specific value. That value will be the sexp base conversion constant plus the base conversion wobble term, $\theta(\text{slog}_a(x))$. Here are some examples of base conversion values I derived using sexp derived from base $\eta^{+}$, which has a wobble when compared to Andy's solution or Dimitrii's solution. $\text{slog}_2(x) - \text{slog}_e(x) = 1.1282$ $\text{slog}_3(x) - \text{slog}_e(x) = -0.1926$ $\text{slog}_{10}(x) - \text{slog}_e(x) = -1.1364$ « 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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