Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Regular slog for base sqrt(2) - Using z=2
Zooming out another factor of 10, the non-circularity of the contours becomes obvious.


Finally, we're zoomed out enough here to see the origin. Notice that we're almost to the interesting part, where our ovals are no longer connected loops. (Technically, they're not connected now, because the imaginary parts increase counter-clockwise, due to the logarithmic singularity. However, the branches are all the same, at least when we calculate the regular slog at 2.)


This is where I can describe the peculiar spacing of the contours. When I take the logarithm of points near the origin, they will towards negative infinity. To get any kind of decent picture of what happens in the left half plane, I had to make my contours bunch up around the origin. And because of how I calculate each region as the logarithm of a region closer to the singularity, I had to effect this strategy from the outset. Therefore, I created a cyclic mapping of the real parts,

This gives me a slope of 0 at the integers, so that I can get values very close to 0 when I get back to the origin. In the next posts, you'll see the effect I was going for.
~ Jay Daniel Fox

Messages In This Thread
RE: Regular slog for base sqrt(2) - Using z=2 - by jaydfox - 11/15/2007, 10:37 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Inspired by the sqrt tommy1729 0 1,624 02/13/2017, 01:11 AM
Last Post: tommy1729
  Some slog stuff tommy1729 15 13,916 05/14/2015, 09:25 PM
Last Post: tommy1729
  tetration base sqrt(e) tommy1729 2 3,668 02/14/2015, 12:36 AM
Last Post: tommy1729
  Regular iteration using matrix-Jordan-form Gottfried 7 9,320 09/29/2014, 11:39 PM
Last Post: Gottfried
  A limit exercise with Ei and slog. tommy1729 0 2,100 09/09/2014, 08:00 PM
Last Post: tommy1729
  A system of functional equations for slog(x) ? tommy1729 3 4,859 07/28/2014, 09:16 PM
Last Post: tommy1729
  [2014] sqrt boundary tommy1729 0 1,917 06/19/2014, 08:03 PM
Last Post: tommy1729
  slog(superfactorial(x)) = ? tommy1729 3 5,358 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 2,709 04/28/2014, 09:23 PM
Last Post: tommy1729
  A simple yet unsolved equation for slog(z) ? tommy1729 0 2,033 04/27/2014, 08:02 PM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)