Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation
#15
Ok, I think I know what you were talking about now.

The primary branchpoints of pentation are going to be where you see the logarithmic singularities in the picture below. These are approximately at
which is also approximately . It is not exact, because the region between -1 and 0 is only approximately (x+1). In other words, if L is a branchpoint of the superlogarithm, then is going to be branchpoint of pentation.

I also plotted two branch systems:
  • A, from branchpoints to imaginary infinities
  • D, from branchpoints to negative infinity

The function being plotted is actually:


Andrew Robbins


Attached Files Image(s)
       
Reply


Messages In This Thread
RE: Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation - by andydude - 10/23/2009, 08:01 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  pentation and hexation sheldonison 8 6,070 2 hours ago
Last Post: Ember Edison
  Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 125 09/09/2019, 10:50 PM
Last Post: tommy1729
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 243 08/18/2019, 02:22 PM
Last Post: sheldonison
  Complex Tetration, to base exp(1/e) Ember Edison 7 887 08/14/2019, 09:15 AM
Last Post: sheldonison
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 1,956 11/07/2017, 11:06 AM
Last Post: sheldonison
Question Analytic matrices and the base units Xorter 2 2,037 07/19/2017, 10:34 AM
Last Post: Xorter
  Base units Xorter 0 1,111 01/22/2017, 10:29 PM
Last Post: Xorter
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 10,343 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,136 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Are tetrations fixed points analytic? JmsNxn 2 2,504 12/14/2016, 08:50 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)