05/16/2017, 03:34 PM
(05/16/2017, 04:09 AM)JmsNxn Wrote: ... It easily follows from this that \( \log^{\circ n}(\lambda^n z + L) \) 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 \( \log_b^{\circ n}(\lambda^n z + L) \) where b is the tetration base.
- Sheldon