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On to C^\infty--and attempts at C^\infty hyper-operations
(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

Messages In This Thread
RE: On to C^\infty--and attempts at C^\infty hyper-operations - by sheldonison - 02/21/2021, 01:38 AM

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