(05/16/2017, 03:34 PM)sheldonison Wrote:(05/16/2017, 04:09 AM)JmsNxn Wrote: ... It easily follows from this that is fully monotone, it uniformly converges to the inverse Schroder function, and therefore the inverse Schroder function is a fully monotone function...Good luck with your paper. We need more rigorous iterated exponentiation papers.

I just wondered what your approach to show the sequence "uniformly converges". Is there an easy theorem, or did you want to go with a more complicated approach something like my lemma5? Just curious. Also, you probably meant where b is the tetration base.

Yeah, I meantt . This is actually a well known result on how to represent the inverse Schroder function. Bo used it before, and that's how I first learnt about it.

Essentially if

and , then not only does

for , where is the Schroder function.

We also get that, if

for , for sufficiently small. This is all you really need.