Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite Pentation (and x-srt-x)
So I tried using regular and natural tetration to fill out the rest of the graph. I almost ignored using bases where because these bases would have 2 fixed points: (1) the upper fixed point would overlap the "blue" region which I already calculated with interpolation (but a good area for comparison), and (2) the lower fixed point would overlap the "green" region which I already calculated with natural iteration (also a good area for comparison).

The only part I used regular tetration for was the "red" region, which corresponds to bases where . Using pure regular iteration from the primary fixed point of the base-a tetrational is real-valued only for integers, and complex-valued everywhere else. So I fudged a little bit to make the graph, I solve the equation and these points are what you see in the "red" region of the graph. I'm pretty sure these are wrong, and that the graph would have to be complex here (if tetrationals for bases less than 1 form complex outputs for real inputs), so it's more of a heuristic than a continuation of the blue curve.


Andrew Robbins

Attached Files
.pdf   x-srt-x-more.pdf (Size: 10.29 KB / Downloads: 392)

Messages In This Thread
Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 09:16 AM
RE: Infinite Pentation (and x-srt-x) - by andydude - 04/13/2009, 05:27 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  pentation and hexation sheldonison 9 13,085 09/18/2019, 02:34 PM
Last Post: sheldonison
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,922 03/20/2018, 12:16 AM
Last Post: tommy1729
  Tetration is pentation. This deserve more thinking. marraco 2 4,812 03/30/2015, 02:54 PM
Last Post: marraco
  [2015] 4th Zeration from base change pentation tommy1729 5 8,052 03/29/2015, 05:47 PM
Last Post: tommy1729
  Mizugadro, pentation, Book Kouznetsov 41 63,624 03/02/2015, 08:13 PM
Last Post: sheldonison
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 15,826 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 6,918 05/06/2014, 09:47 PM
Last Post: tommy1729
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 9,135 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 5,362 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 6,817 07/15/2011, 02:23 AM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)