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.
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.