Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
tetration base conversion, and sexp/slog limit equations
I think there's a reasonable chance the higher derivatives will misbehave, and I think there's a reasonable chance the limit for the sexp limit may not even converge. The graph below is converting to base 1.6, from base 1.4453

The anomaly in the third derivative of the graph seems larger than the error term. I need to do some more error term estimates, and also see if converting from other bases (1.45 and 1.485, the other two spreadsheets I have generated), give similar results. Smaller bases are much more sensitive to the problems, which aren't seen in the third derivative for base e. The anomaly in the third derivative is caused by the fact that the inflection point for this sexp estimate is on the "wrong" side of the critical section -- the inflection point is on the right of the critical section instead of the left of the critical section.
[Image: base_16.gif]

I suspect that with a base close enough to converted from a base even closer to , even the first derivative will eventually show an anomaly, which might invalidate the error term equation estimates I derived. I saw a similar result converting from base 1.45 to base 1.485, where the inflection point wound up on the "wrong" side of the critical section, also causing the anomaly. But in the base 1.6 case, the results seem to be outside the range of the error term.

All this is hypothetical. I probably need to download a version of mathematica to generate the results in higher precision arithmetic to be certain, but maybe Jay is correct. Maybe the sexp base conversions are always going to have anomalies, the question is how large they are.

Messages In This Thread
RE: tetration base conversion, and sexp/slog limit equations - by sheldonison - 02/28/2009, 05:56 AM
Is it analytic? - by sheldonison - 12/22/2009, 11:39 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Moving between Abel's and Schroeder's Functional Equations Daniel 1 723 01/16/2020, 10:08 PM
Last Post: sheldonison
  Complex Tetration, to base exp(1/e) Ember Edison 7 3,598 08/14/2019, 09:15 AM
Last Post: sheldonison
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,681 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 1,913 09/06/2016, 04:23 PM
Last Post: tommy1729
  Taylor polynomial. System of equations for the coefficients. marraco 17 19,150 08/23/2016, 11:25 AM
Last Post: Gottfried
  Dangerous limits ... Tommy's limit paradox tommy1729 0 2,191 11/27/2015, 12:36 AM
Last Post: tommy1729
  tetration limit ?? tommy1729 40 55,312 06/15/2015, 01:00 AM
Last Post: sheldonison
  Some slog stuff tommy1729 15 14,947 05/14/2015, 09:25 PM
Last Post: tommy1729
  Totient equations tommy1729 0 2,051 05/08/2015, 11:20 PM
Last Post: tommy1729
  Bundle equations for bases > 2 tommy1729 0 2,089 04/18/2015, 12:24 PM
Last Post: tommy1729

Users browsing this thread: 2 Guest(s)