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Carlson's theorem and tetration
#8
(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 for some function 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 , right? For "any" z seems too restrictive: , for example, does have many -values for which its iteration diverges, but these do not show up in the range of the tetrational .

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Messages In This Thread
Carlson's theorem and tetration - by mike3 - 08/19/2010, 08:43 AM
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 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 mike3 - 08/20/2010, 08:26 PM

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