Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
complex iteration (complex "height")
#19
I tried to do analytically one case:

lower fixed point
we get the base by
if then



but :










At this point I do not know what to do with limits -how do You apply n to iterating logarithms, and at the same time to iteration of exponentiation of 1/e inside it? If we could move limit inside, than:



And



for all n, so

which equals



I know it is not complex but real...

Must be a mistake with the limits, but looks nice still...

If someone could explain me on this example how I should have proceeded after the place where I got to limit taking inside iterated logarithm, I promise never to make the same mistake.

If we take the same but:



Then I have to go through the whole procedure again.
In this case, instead of we will have 0, and + before tower as:





this seems to equal 1. So with negative height:






Ivars
Reply


Messages In This Thread

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex or Real numbers more important? Daniel 0 131 12/22/2019, 10:36 AM
Last Post: Daniel
  Complex Tetration, to base exp(1/e) Ember Edison 7 2,205 08/14/2019, 09:15 AM
Last Post: sheldonison
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 12,395 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Negative, Fractional, and Complex Hyperoperations KingDevyn 2 6,378 05/30/2014, 08:19 AM
Last Post: MphLee
  new results from complex dynamics bo198214 25 34,639 02/25/2013, 01:42 AM
Last Post: sheldonison
  Complex Tetration Balarka Sen 16 22,321 02/21/2013, 02:23 PM
Last Post: sheldonison
  (MSE) periods in (z*exp(z*exp(...))) for complex z Gottfried 0 2,885 04/16/2012, 10:24 AM
Last Post: Gottfried
  Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 2,901 09/04/2011, 05:59 AM
Last Post: Gottfried
  Real and complex behaviour of the base change function (was: The "cheta" function) bo198214 39 52,868 08/13/2011, 06:33 PM
Last Post: bo198214
  Fractional iteration of x^2+1 at infinity and fractional iteration of exp bo198214 10 16,884 06/09/2011, 05:56 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)