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 Math overflow question on fractional exponential iterations sheldonison Long Time Fellow Posts: 684 Threads: 24 Joined: Oct 2008 03/28/2018, 07:57 PM (This post was last modified: 03/28/2018, 09:33 PM by sheldonison.) Dmytro Taranovsky asks in his post, https://mathoverflow.net/questions/28381...rent-bases ... " ... Let a and b be real numbers above e^{1/e}, and c exp(1/e), then my conjecture is that the limit holds.  Unfortunately, Peter Walker's solution is also conjectured to be nowhere analytic; see: https://math.stackexchange.com/questions...lytic-slog (2) That for Kneser's solution, there are counter examples and the limit does not hold, even with the restriction that c\;\exp_b^d(x)$ (3) Given any analytic solution for base(a), then if we desire a tetration solution for base(b) which has the desired property then I conjecture that the tetration base b is nowhere analytic!  The conjecture is also that the slog for b would be given by a modification of Peter Walker's h function. - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread Math overflow question on fractional exponential iterations - by sheldonison - 03/28/2018, 07:57 PM RE: Math overflow question on fractional exponential iterations - by sheldonison - 03/29/2018, 10:13 PM RE: Math overflow question on fractional exponential iterations - by JmsNxn - 03/30/2018, 07:37 PM RE: Math overflow question on fractional exponential iterations - by sheldonison - 03/31/2018, 04:19 AM RE: Math overflow question on fractional exponential iterations - by JmsNxn - 04/01/2018, 03:09 AM

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