eta as branchpoint of tetrational
#23
(06/07/2011, 05:47 PM)bo198214 Wrote: Wow, Sheldon, thats such a great overview!

Only one clarification: What means ~=? I guess it means not equal.
but then your "new function" Im(z)=8.6 must read "Im(f(z))=0" instead of ~=0?

It must be symmetric about the real axis.
I have to update that typo in my picture. Im(f(z))~=0 except at the real axis. For the NewFunc (Kneser mapping), Im(f(z))~=0 means that Im(f(z)) is wobbling very close to zero, but not equal to zero.
Quote:But I am really amazed how quickly you develop your code for new functions!

Say, is your "new function" analytic continuable through base eta?
I haven't calculated the Fatou function yet, but now that I have drawn the pictures, it should be easy to calculate (easy compared to a Kneser Riemann mapping), and convergence precision should improve much much quicker than the Kneser Riemann mapping. It will still be an iterative mapping, iteratively generating each of the two theta(z) functions from the other superfunction, and the other theta(z) function. Because there is so much overlap where both theta(z) functions are analytic, no intermediate "sexp" function will be required to generate the mapping.

Yes, the Kneser mapping "newfunc", for B<eta is continuable through to eta, if you provide a corresponding continuous sequence of upper superfunctions, from B=sqrt(2) to B=eta. Of course, the imag period goes to infinity at B=eta. In each of these upper superfunctions, there will be suitable contour which can be Kneser mapped, to generate a real valued function for z>-2, which will have singularities at z=-2,-3,-4 .....

Thanks for the compliments.
- Shel


Messages In This Thread
eta as branchpoint of tetrational - by mike3 - 06/02/2011, 01:55 AM
RE: eta as branchpoint of tetrational - by mike3 - 06/03/2011, 10:57 PM
RE: eta as branchpoint of tetrational - by mike3 - 06/04/2011, 09:08 AM
RE: eta as branchpoint of tetrational - by mike3 - 06/04/2011, 09:50 AM
RE: eta as branchpoint of tetrational - by sheldonison - 06/07/2011, 05:54 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Base 'Enigma' iterative exponential, tetrational and pentational Cherrina_Pixie 4 17,092 07/02/2011, 07:13 AM
Last Post: bo198214
  regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) JmsNxn 5 15,011 06/15/2011, 12:27 PM
Last Post: Gottfried
  Coefficients of Tetrational Function mike3 3 12,618 04/28/2010, 09:11 PM
Last Post: andydude



Users browsing this thread: 1 Guest(s)