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 Kneser's Super Logarithm sheldonison Long Time Fellow Posts: 623 Threads: 22 Joined: Oct 2008 01/28/2010, 10:08 PM (01/28/2010, 08:52 PM)mike3 Wrote: So then it would seem to agree with the Kouznetsov function, then, wouldn't it, i.e. the $\operatorname{tet}_e(z)$ function developed this way decays to approximately $0.318 \pm 1.337i$ as $z \rightarrow \pm i \infty$? Hmm. Does this Kneser method work for other bases, too?Yes, and Yes. I don't think anyone's tried it though. Quote:Can it be used at a complex base, e.g. $2 + 1.5i$? You could always generate the inverse Abel function from the fixed point for the complex base. But if f(z) is real valued, f(z+1) would have a complex value, so the Kneser mapping couldn't convert the Abel function into a real valued tetration. But it seems like it could generate an analytic complex base tetration where sexp(-1)=0, sexp(0)=1, sexp(1)=2+1.5i, sexp(2)=(2+1.5i)^(2+1.5i) and sexp(-2,-3,-4...)=singularity.... « Next Oldest | Next Newest »

 Messages In This Thread Kneser's Super Logarithm - by bo198214 - 11/19/2008, 02:20 PM RE: Kneser's Super Logarithm - by bo198214 - 11/19/2008, 03:25 PM RE: Kneser's Super Logarithm - by sheldonison - 01/23/2010, 01:01 PM RE: Kneser's Super Logarithm - by mike3 - 01/25/2010, 06:35 AM RE: Kneser's Super Logarithm - by sheldonison - 01/25/2010, 07:42 AM RE: Kneser's Super Logarithm - by mike3 - 01/26/2010, 06:24 AM RE: Kneser's Super Logarithm - by sheldonison - 01/26/2010, 01:22 PM RE: Kneser's Super Logarithm - by mike3 - 01/27/2010, 06:28 PM RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 08:30 PM RE: Kneser's Super Logarithm - by mike3 - 01/28/2010, 08:52 PM RE: Kneser's Super Logarithm - by sheldonison - 01/28/2010, 10:08 PM RE: Kneser's Super Logarithm - by mike3 - 01/29/2010, 06:43 AM RE: Kneser's Super Logarithm - by bo198214 - 01/26/2010, 11:19 PM RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 07:51 PM RE: Kneser's Super Logarithm - by bo198214 - 11/22/2008, 06:11 PM RE: Kneser's Super Logarithm - by bo198214 - 11/23/2008, 01:00 PM

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