07/29/2009, 08:20 AM
(This post was last modified: 07/29/2009, 08:33 AM by Base-Acid Tetration.)
as you go left along the real axis: singularity at z=-2, and then bounce back up, then branch cut? so confusing... why?
of the tetration's riemann surface, i expected a logarithmic branch point because of the logarithm's involvement in tetration - i expected the ray z<=-2 is a cut of the superlogarithm.
http://en.wikipedia.org/wiki/File:Rieman...ce_log.jpg
Yes, I understand that a function doesn't need to blow up near the branch point. The square root function is an example that has a branch point at 0.
But I was expecting something like a logarithmic branch cut.
of the tetration's riemann surface, i expected a logarithmic branch point because of the logarithm's involvement in tetration - i expected the ray z<=-2 is a cut of the superlogarithm.
Kouznetsov Wrote:some of its Riemann surfaces are plotted atI was looking for something like this (a parametric plot of the imaginary part of a function) at wikipedia:
http://www.ils.uec.ac.jp/~dima/PAPERS/2009fractae.pdf
http://en.wikipedia.org/wiki/File:Rieman...ce_log.jpg
Kouznetsov Wrote:Henryk, may I post here the plots of sqrt(exp) and sqrt(!) in order to show that a function has no need to blow up in vicinity of its branch point?
Yes, I understand that a function doesn't need to blow up near the branch point. The square root function is an example that has a branch point at 0.
But I was expecting something like a logarithmic branch cut.
