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05/16/2017, 08:46 PM
(This post was last modified: 05/16/2017, 08:48 PM by JmsNxn.)
(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
 = z_0)
and
| < 1)
, then not only does
 - z_0}{\lambda^n} \to \Psi(z))
for
, where
is the Schroder function.
We also get that, if
 \to \Psi^{-1}(z))
for
, for
sufficiently small. This is all you really need.
