Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Change of base formula for Tetration
#13
andydude Wrote:PS. Just a side-note, I understand that () and (slog) are different functions, but if you swap them in the above equations, then you get the formula for iterated exponentials, which I found interesting.

Actually, the connection is very important. In fact, it's actually the reason that we can solve for . Technically, even if you tetrate an infinite number of times, you can't get above the asymptote. So really, the function is a limiting case of , with k an appropriate factor that I'll define in a later post. I have a rough idea of how to explain it, but I don't want to describe it incorrectly and confuse anyone.

Anyway, once you start exponentially iterating values smaller than eta, you can never get above their associated asymptotes. However, if you start at positive infinity (which means taking a limit), and use iterated logarithms, you can work your way back down to the higher asymptote. That's why I think your notation actually works a little better, even though we're essentially describing the same thing.

By the way, how much of what I'm explaining in my various posts is already known? Some of it I've seen before, and some of it I've seen in an alternative format that masked the meaning, and some of it seems original, but I can't really be sure. I'm wondering if I'm on to anything publishable. I've never been published, so it would be cool if I were on to something.
~ Jay Daniel Fox
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 jaydfox - 08/13/2007, 06:34 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

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 615 08/14/2019, 09:15 AM
Last Post: sheldonison
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,259 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,093 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Extrapolated Faá Di Bruno's Formula Xorter 1 1,742 11/19/2016, 02:37 PM
Last Post: Xorter
  [2015] 4th Zeration from base change pentation tommy1729 5 5,008 03/29/2015, 05:47 PM
Last Post: tommy1729
  Conjecture on semi-exp base change [2015] tommy1729 0 1,493 03/24/2015, 03:14 PM
Last Post: tommy1729
  tetration base sqrt(e) tommy1729 2 2,931 02/14/2015, 12:36 AM
Last Post: tommy1729
  Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 2,582 02/13/2015, 02:26 PM
Last Post: Gottfried
  tetration base > exp(2/5) tommy1729 2 2,720 02/11/2015, 12:29 AM
Last Post: tommy1729
  about power towers and base change tommy1729 7 7,139 05/04/2014, 08:30 AM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)