Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Real and complex behaviour of the base change function (was: The "cheta" function)
To demonstrate that there are singularities all along the positive real line, I will show the first three, with lines connecting them to x=1. I will show several more, without exponentiating them, just to give you an idea of where they are. The color scheme is the same as before: blue is the original image, cyan is the first exponentiation, yellow-green is the second, red is the third.

Note that I did the first 100 such singularities, yet they get so close together that the dots just overlap in this graph:


And now a zoomout. Note that, due to the large real part of the yellow line (up to about 16 in places), the red line will be an arc with a radius of several million in places. I could zoom out to show this, but I trust everyone can imagine it.

~ Jay Daniel Fox

Messages In This Thread
RE: Real and complex behaviour of the base change function (was: The "cheta" function - by jaydfox - 08/15/2009, 11:02 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 887 08/14/2019, 09:15 AM
Last Post: sheldonison
  Is there a function space for tetration? Chenjesu 0 146 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,353 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Degamma function Xorter 0 638 10/22/2018, 11:29 AM
Last Post: Xorter
  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
  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
  Taylor series of cheta Xorter 13 10,753 08/28/2016, 08:52 PM
Last Post: sheldonison
  2 real fixpoints again ....... tommy1729 10 8,045 02/23/2016, 10:17 PM
Last Post: tommy1729
  Should tetration be a multivalued function? marraco 17 14,716 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 3,183 01/10/2016, 06:14 PM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)