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 A conjectured uniqueness criteria for analytic tetration JmsNxn Ultimate Fellow Posts: 889 Threads: 110 Joined: Dec 2010 02/17/2017, 05:21 AM So I posted here the most solvable version of your question I could think of on MO http://mathoverflow.net/questions/262444...-functions If this statement turns out to be true then it unequivocably proves that not only is the schroder iteration method the only completely monotone solution to tetration; but also for pentation, sexation, and so on. I'm confident this statement follows too. This would give a really good real valued criterion for the uniqueness of $\alpha \uparrow^n x$ for $\alpha \in (1,\eta)$ and $x \in \mathbb{R}^+$. I hope someone in the more general mathematics community might be able to help us. « Next Oldest | Next Newest »

 Messages In This Thread A conjectured uniqueness criteria for analytic tetration - by Vladimir Reshetnikov - 10/30/2016, 11:02 PM RE: A conjectured uniqueness criteria for analytic tetration - by sheldonison - 11/01/2016, 02:08 AM RE: A conjectured uniqueness criteria for analytic tetration - by tommy1729 - 11/30/2016, 01:26 AM RE: A conjectured uniqueness criteria for analytic tetration - by sheldonison - 12/01/2016, 12:59 PM RE: A conjectured uniqueness criteria for analytic tetration - by tommy1729 - 12/07/2016, 01:25 PM RE: A conjectured uniqueness criteria for analytic tetration - by Vladimir Reshetnikov - 01/11/2017, 12:03 AM RE: A conjectured uniqueness criteria for analytic tetration - by Vladimir Reshetnikov - 01/15/2017, 06:19 PM RE: A conjectured uniqueness criteria for analytic tetration - by JmsNxn - 01/23/2017, 07:03 AM RE: A conjectured uniqueness criteria for analytic tetration - by JmsNxn - 01/24/2017, 08:30 PM RE: A conjectured uniqueness criteria for analytic tetration - by Vladimir Reshetnikov - 01/25/2017, 12:44 AM RE: A conjectured uniqueness criteria for analytic tetration - by bo198214 - 01/25/2017, 06:26 PM RE: A conjectured uniqueness criteria for analytic tetration - by tommy1729 - 02/03/2017, 01:23 PM RE: A conjectured uniqueness criteria for analytic tetration - by JmsNxn - 01/25/2017, 09:46 PM RE: A conjectured uniqueness criteria for analytic tetration - by JmsNxn - 02/17/2017, 05:21 AM

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