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tetration from alternative fixed point
(05/24/2010, 03:03 PM)sheldonison Wrote: ....I do see that the secondary superfunction would lead to a sexp with a total of 6*pi*i windings around the singularity at -2.

I'll post a picture of the 3*pi*i contour line when I get the arithmetic working, analogous to the picture I posted of the contour line from the primary fixed point,
I haven't gotten the contour picture yet (and that would be the contours of the complex valued superfunction before the Riemann mapping), but I wanted to point at that 6*pi*i windings (after the Riemann mapping, which I have virtually no hope of computing) around the singularity of sexp_secondary(z=-2) is consistent with the taylor series for the sexp_secondary(z) at z=-1 having a lowest power term of z^3. The first and second derivatives would both be zero at f(z=-1). So I still think it might work, and might be analytic, although perhaps not terribly interesting, since the graph would be very very wobbly, with an inflection point and a derivative of zero at integers>=-1, z=-1,0,1,2,3 ..... Smile
- Shel

Messages In This Thread
RE: tetration from alternative fixed point - by sheldonison - 06/03/2010, 04:13 AM

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