Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Change of base formula for Tetration
#41
(05/03/2009, 10:20 PM)tommy1729 Wrote: ???

how does change of base formula for tetration and exp(z) -1 relate ???

i would recommend -- in case this is important and proved -- that more attention is given to it on the forum and/or FAQ
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/tetrationforu...hp?tid=236.
Reply


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, 11:21 AM
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

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 4 438 05/08/2019, 06:20 PM
Last Post: Ember Edison
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,221 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,053 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Extrapolated Faá Di Bruno's Formula Xorter 1 1,688 11/19/2016, 02:37 PM
Last Post: Xorter
  [2015] 4th Zeration from base change pentation tommy1729 5 4,906 03/29/2015, 05:47 PM
Last Post: tommy1729
  Conjecture on semi-exp base change [2015] tommy1729 0 1,455 03/24/2015, 03:14 PM
Last Post: tommy1729
  tetration base sqrt(e) tommy1729 2 2,880 02/14/2015, 12:36 AM
Last Post: tommy1729
  Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 2,519 02/13/2015, 02:26 PM
Last Post: Gottfried
  tetration base > exp(2/5) tommy1729 2 2,660 02/11/2015, 12:29 AM
Last Post: tommy1729
  about power towers and base change tommy1729 7 7,002 05/04/2014, 08:30 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)