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Solving tetration for base 0 < b < e^-e
#13
(09/12/2009, 09:04 PM)mike3 Wrote: So then since neither of those worked, it seems all we're left with is the Ansus formula and the Cauchy integral (but determining the correct contours and asymptotic behavior, now that's the rub...).

I dont think, one can say that the regular iteration didnt work.
Its rather that it doesnt match your requirement to have a singularity at -2.
Though this requirement is quite apparent for real-valued functions, because we necessarily use the real branch of the logarithm, the necessity is not so clear for complex valued functions, where there is free choice of the branch of the logarithm.

It sounds anyway strange to prefer a singular tetrational over an entire tetrational if there is not the demand of real values.

Btw.: Kouznetsov's Contour integral method is rather applicable between two conjugate non-real fixed points. I doubt that you can use the idea for a real 2-cycle.
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RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM

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