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 ...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.

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 )

(05/03/2009, 10:20 PM)tommy1729 Wrote: furthermore , i asked how change of base formula for tetration and exp(z) - 1 relate ?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.

that isnt answered ...

(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.