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 Carlson's theorem and tetration mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 08/21/2010, 08:08 PM (08/21/2010, 08:36 AM)tommy1729 Wrote: (08/20/2010, 08:35 PM)mike3 Wrote: Quote:I guess it can be generalized to arbitrary regular superfunctions as they are always of the form $\eta(\pm e^{\kappa z})$ for some function $\eta$ analytic at 0. Yes, provided the fixed point is attracting and positive real. i believe we need oo to be repelling and f^^n(z) converging for lim n-> oo and any z too. You mean $f^n(z)$, right? For "any" z seems too restrictive: $f(z) = \eta^z$, for example, does have many $z$-values for which its iteration diverges, but these do not show up in the range of the tetrational $^z \eta$. « Next Oldest | Next Newest »

 Messages In This Thread Carlson's theorem and tetration - by mike3 - 08/19/2010, 08:43 AM RE: Carlson's theorem and tetration - by tommy1729 - 08/19/2010, 10:56 PM RE: Carlson's theorem and tetration - by bo198214 - 08/20/2010, 12:21 PM RE: Carlson's theorem and tetration - by mike3 - 08/20/2010, 08:35 PM RE: Carlson's theorem and tetration - by tommy1729 - 08/21/2010, 08:36 AM RE: Carlson's theorem and tetration - by mike3 - 08/21/2010, 08:08 PM RE: Carlson's theorem and tetration - by bo198214 - 08/22/2010, 05:12 AM RE: Carlson's theorem and tetration - by sheldonison - 08/20/2010, 05:08 PM RE: Carlson's theorem and tetration - by mike3 - 08/20/2010, 08:26 PM

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