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



and

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 ??

regards

tommy1729
Reply


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
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 153 09/09/2019, 10:38 PM
Last Post: tommy1729
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,601 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 633 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Hyper-volume by integration Xorter 0 1,223 04/08/2017, 01:52 PM
Last Post: Xorter
  Hyper operators in computability theory JmsNxn 5 3,454 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,335 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 35,380 09/02/2016, 02:11 AM
Last Post: tommy1729
  The bounded analytic semiHyper-operators JmsNxn 2 3,271 05/27/2016, 04:03 AM
Last Post: JmsNxn
  on constructing hyper operations for bases > eta JmsNxn 1 2,445 04/08/2015, 09:18 PM
Last Post: marraco
  Bounded Analytic Hyper operators JmsNxn 25 18,025 04/01/2015, 06:09 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)