Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Regular slog for base sqrt(2) - Using z=2
#11
Amazing fractals.

So is there now final formula for all branches of h(z) = e^-Wk(-ln(z))? So easy so I can use Wolfram function evaluation web page? Would it work also for analytic continuation of h(z) in the range z>e^1/e and or z<0? (by using ln(-x)= ln(x) +- pi*I*(2k+1), k>=0)?

Ivars
Reply
#12
bo198214 Wrote:How can one find the singularities of and the complex fixed points of in your drawing?

Actually, the easiest way is to look at the definition of the rslog itself. We know the two primary singularities are at 2 and 4. Therefore, we can find one tier of "images" of these two singularities with:



We can find the next tier of images by simply repeating this process: every branch of two iterated logarithms:



This can be repeated indefinitely. Indeed, going back to the definition of the rslog, if we look at a solution for a finite n, then we can only repeat the process n times, and only for the images of the fixed point at 2. The fixed point at 4 is only a singularity when n goes to infinity.

And looking at j, k, etc., we can see that setting the innermost branches to 0 allows us to generalize a shorter sequence with the infinite sequence. We can then specify a singularity by indicating if its an image of the upper or lower fixed point, and then specify its infinite sequence of branch choices, starting from the outermost, with the sequence truncated if the branch choices are all 0 beyond a certain iterated logarithm.
~ Jay Daniel Fox
Reply
#13
jaydfox Wrote:It's not 18*I, it's

Right, sorry, thanks.
Reply
#14
(11/27/2007, 07:10 PM)andydude Wrote:
jaydfox Wrote:It's not 18*I, it's

Right, sorry, thanks.

If one uses other bases in the interval 1<b<exp(exp(-1)) it seems better to express it more generally as
where b is the base, and the upper horizontal asymptote is at
Gottfried Helms, Kassel
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Inspired by the sqrt tommy1729 0 1,264 02/13/2017, 01:11 AM
Last Post: tommy1729
  Some slog stuff tommy1729 15 10,938 05/14/2015, 09:25 PM
Last Post: tommy1729
  tetration base sqrt(e) tommy1729 2 3,055 02/14/2015, 12:36 AM
Last Post: tommy1729
  Regular iteration using matrix-Jordan-form Gottfried 7 7,858 09/29/2014, 11:39 PM
Last Post: Gottfried
  A limit exercise with Ei and slog. tommy1729 0 1,785 09/09/2014, 08:00 PM
Last Post: tommy1729
  A system of functional equations for slog(x) ? tommy1729 3 4,067 07/28/2014, 09:16 PM
Last Post: tommy1729
  [2014] sqrt boundary tommy1729 0 1,629 06/19/2014, 08:03 PM
Last Post: tommy1729
  slog(superfactorial(x)) = ? tommy1729 3 4,609 06/02/2014, 11:29 PM
Last Post: tommy1729
  [stuck] On the functional equation of the slog : slog(e^z) = slog(z)+1 tommy1729 1 2,253 04/28/2014, 09:23 PM
Last Post: tommy1729
  A simple yet unsolved equation for slog(z) ? tommy1729 0 1,729 04/27/2014, 08:02 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)