Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
holomorphic binary operators over naturals; generalized hyper operators
(07/19/2012, 04:44 PM)JmsNxn Wrote: We start by defining a sequence of analytic functions that obey the following rules:


Necessarily; these functions can be arbitrary and they pose the true uniqueness criterion. Nonetheless we suggest these functions and give a plausible solution.

Reason for this is it has fast convergence and satisfies the required conditions.

Now we perform a trick. Considering hyper operators; which are written by the following:

and the identity of for any natural is .

We get the usual sequence where zero is addition, one is multiplication, two is exponentiation, etc... We then write that complex operators are products of natural operators with complex exponents. Here; is as before.

Dont you need to prove the identity of the infinite product ?

e.g. does the infinite product formula hold for x + y and x*y ??



Messages In This Thread
RE: holomorphic binary operators over naturals; generalized hyper operators - by tommy1729 - 07/19/2012, 10:16 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  The Generalized Gaussian Method (GGM) tommy1729 2 337 10/28/2021, 12:07 PM
Last Post: tommy1729
  Some "Theorem" on the generalized superfunction Leo.W 44 9,164 09/24/2021, 04:37 PM
Last Post: Leo.W
  On my old fractional calculus approach to hyper-operations JmsNxn 14 3,121 07/07/2021, 07:35 AM
Last Post: JmsNxn
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 8,070 05/26/2021, 11:55 PM
Last Post: MphLee
  A Holomorphic Function Asymptotic to Tetration JmsNxn 2 1,101 03/24/2021, 09:58 PM
Last Post: JmsNxn
  hyper 0 dantheman163 2 5,283 03/09/2021, 10:28 PM
Last Post: MphLee
  On to C^\infty--and attempts at C^\infty hyper-operations JmsNxn 11 3,731 03/02/2021, 09:55 PM
Last Post: JmsNxn
  Generalized phi(s,a,b,c) tommy1729 6 2,019 02/08/2021, 12:30 AM
Last Post: JmsNxn
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 3,701 09/09/2019, 10:38 PM
Last Post: tommy1729
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 14,899 06/10/2019, 04:29 AM
Last Post: Ember Edison

Users browsing this thread: 1 Guest(s)