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Change of base formula for Tetration
#43
(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 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 where , 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, . Here are some examples of base conversion values I derived using sexp derived from base , which has a wobble when compared to Andy's solution or Dimitrii's solution.



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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 sheldonison - 05/05/2009, 01:29 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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