Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Comparing the Known Tetration Solutions
#2
If by my solution you mean through parabolic iteration of and by Daniel's you mean through hyperbolic iteration of , then yes, I'd be happy to provide some high-quality graphics and numerical tables. I still need to re-read Jay's solution, since it seems dependent on the super-logarithmic constant which I don't understand yet. Also you brought up an interesting point that may prevent comparison of all methods, since some methods work over non-overlapping intervals.

Tetration can be divided into several intervals in terms of what values of x in are valid for that definition: the parabolic point , the hyperbolic interval , and I suppose would you could call the elliptic? interval , which is what my definition of the super-logarithm is valid for. These are all closely tied to the interval of convergence of the infinite hyper-power which was found almost 230 years ago. Smile My how time has passed...

Andrew Robbins
Reply


Messages In This Thread
RE: computing the iterated exp(x)-1 - by andydude - 08/17/2007, 11:20 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/17/2007, 11:38 PM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/17/2007, 11:45 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 12:19 AM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 08:19 AM
RE: computing the iterated exp(x)-1 - by andydude - 08/18/2007, 09:35 AM
RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 11:59 AM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 03:49 PM
RE: computing the iterated exp(x)-1 - by jaydfox - 08/19/2007, 12:50 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Solutions to f ' (x) = f(f(x)) ? tommy1729 1 2,157 08/12/2013, 12:10 AM
Last Post: tommy1729
  Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) Gottfried 91 85,640 03/03/2011, 03:16 PM
Last Post: Gottfried
  Infinite towers & solutions to Lambert W-function brangelito 1 3,610 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)