Change of base formula for Tetration - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Change of base formula for Tetration ( /showthread.php?tid=14) |

RE: Change of base formula for Tetration - sheldonison - 05/05/2009
(05/03/2009, 10:20 PM)tommy1729 Wrote: ???I 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. In this equation, converges to n plus the base conversion constant. This base conversion will have a small 1-cyclic periodic wobble, , when compared to Dimitrii's solution. 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 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/tetrationforum/showthread.php?tid=236. RE: Change of base formula for Tetration - tommy1729 - 05/05/2009
(05/05/2009, 11:21 AM)sheldonison Wrote:(05/03/2009, 10:20 PM)tommy1729 Wrote: ???I agree that the base conversion problem is very interesting, and needs more attention. 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 RE: Change of base formula for Tetration - sheldonison - 05/05/2009
(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/tetrationforum/showthread.php?tid=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 ?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 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. RE: Change of base formula for Tetration - bo198214 - 05/05/2009
(05/05/2009, 01:29 PM)sheldonison Wrote: the base conversion wobble term, Do we make this the official name? |