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 Base -1 sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 06/02/2015, 05:27 PM (This post was last modified: 06/02/2015, 11:08 PM by sheldonison.) (06/02/2015, 01:08 PM)marraco Wrote: (06/01/2015, 03:46 AM)sheldonison Wrote: Here is what analytic sexp base(-1) looks like at the real axis. Wonderful! Did you tried negative bases close to zero?Yes, though I'm not really getting useful results yet. The algorithm works with $k=\ln(\ln(b))+1$ For b=0.5, that would be $k\approx 0.633487+\pi i$, where we iterate $z \mapsto \exp(z)-1+k$. Right now, the closest I can get to tetration base=0.5 with good convergence is b=0.5+0.39i, which is k=0.782+2.173i. I'm having several different kinds of problems with these bases, though I hope I will eventually get full convergence for some bases with imag(k)=pi, though convergence will still be limited for bases with indifferent fixed points like $b=\exp(-e)$ - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread Base -1 - by marraco - 05/21/2015, 06:31 PM RE: Base -1 - by sheldonison - 05/22/2015, 05:28 AM RE: Base -1 - by sheldonison - 06/01/2015, 03:46 AM RE: Base -1 - by marraco - 06/02/2015, 01:08 PM RE: Base -1 - by sheldonison - 06/02/2015, 05:27 PM

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