02/21/2021, 01:38 AM

(02/16/2021, 08:40 AM)JmsNxn Wrote: So I posted a proof of before I started working today...

I am in the process of rewriting my entire paper to focus on hyper-operations; whereby it's a long proof by induction. But the initial step is to prove that this tetration is . Now I can most definitely show this tetration is ; the trouble I'm having is making the proof as general as possible; so that we can create a proof by induction showing is .

Hi James,

I like your paper. I would suggest generating an infinite sequence of entire functions, perhaps defined as follows; this is slightly modified from your approach where this = JmsNxn phi(s+1)

we could start with

this asymptotically approaches exp(s) as gets arbitrarily negative,

also asymptotically approaches exp(s) as gets arbitrarily negative

James has proven that is entire, and I think each of these phi functions is also entire, and each would probably lead to an function which is also only defined at the real axis; details tbd...

- Sheldon