02/01/2021, 11:20 PM
(02/01/2021, 09:31 PM)JmsNxn Wrote: I'd love to talk about those ideas! I always liked Andy's slog, but I'm horrible with matrices so it never made much sense (other than the broad motions). Has it ever actually been shown to be analytic? I really enjoyed Peter Walker's paper too.
As far as we know (here) it has not been shown to be analytic.
On the other hand if it converges to a C^oo function then it is analytic because it is a taylor series.
I mentioned at least 1 method that forces to solve infinite systems of linear equations however it has not been proven to give a nonzero-radius hence not proven c^oo or even convergeant let alone analytic.
I even discovered a set of equations that turned out to be truncated equations equivalent to Andy/Peter , hence a rediscovery in some way.
Unfortunately my other viewpoint was not helpful.
Analytic tetration is a difficult subject !
Btw I posted a correction to the NBLR method ( the recent closed form based on phi and lambertW).
You should probably want to see it.
regards
tommy1729