Thread Rating:
  • 1 Vote(s) - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e))
#2
Gottfried Wrote:The plot shows this (in principle, it is far too granular!) by colors for imag(s) where t = x + I*y. Where the color is black, purely real values occur for s, because black means imag(s)~0. The real value of s is not visible from that plot, but I showed in my other graph, that it ranges
I've just got another image with a higher resolution and stronger rescaling of imag(s)


The black's are still areas in the plot, and I'd like to see them as lines.
The closer the argument real(t) is at zero, the more solutions for real(s)>e^(1/e) are available, and also the absolute values real(s) increase strongly(which again cannot be seen in the graph)
The tick-marks for x and y-axes are not correct in the plot; the range is the right half of the complex half-unit-square.

I'd like to understand, whether the imaginary nulls of the function f(x)=x^(1/x) form continuous lines...

Gottfried


[update] plot removed, improved plot see next post
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: Tetration below 1 - by Gottfried - 09/09/2007, 07:04 AM
RE: The Complex Lambert-W - by Gottfried - 09/09/2007, 04:54 PM
RE: The Complex Lambert-W - by andydude - 09/10/2007, 06:58 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 2,117 11/07/2017, 11:06 AM
Last Post: sheldonison
  2 real fixpoints again ....... tommy1729 10 8,420 02/23/2016, 10:17 PM
Last Post: tommy1729
  A new set of numbers is necessary to extend tetration to real exponents. marraco 7 8,620 03/19/2015, 10:45 PM
Last Post: marraco
  Real-analytic tetration uniqueness criterion? mike3 25 19,805 06/15/2014, 10:17 PM
Last Post: tommy1729
  About real limits tommy1729 1 2,270 09/23/2013, 09:24 PM
Last Post: tommy1729
  Solutions to f ' (x) = f(f(x)) ? tommy1729 1 2,174 08/12/2013, 12:10 AM
Last Post: tommy1729
  Real and complex behaviour of the base change function (was: The "cheta" function) bo198214 39 48,816 08/13/2011, 06:33 PM
Last Post: bo198214
  The imaginary tetration unit? ssroot of -1 JmsNxn 2 5,166 07/15/2011, 05:12 PM
Last Post: JmsNxn
  Tetration and imaginary numbers. robo37 2 5,147 07/13/2011, 03:25 PM
Last Post: robo37
  Infinite tetration of the imaginary unit GFR 40 51,785 06/26/2011, 08:06 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)