Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
holomorphic binary operators over naturals; generalized hyper operators
#14
Right now I'm writing out some assumptions we have to put away.

For example:



This implies that is not analytic because it is 2 for all s with real part greater than or equal to 1 and 3 when s is 0.

Another one is that any continuous segment of operators is commutative or associative all the operators have to be. As well; operators in a continuous segment cannot have the same identity.

The functional requirement is the following:



where we have:









And is as before.

I can obtain as a taylor series using lagrange inversion. So all of these functions are theoretically computable besides which is in . So the requirement is restricted to it. I'm writing this all out trying to solve for the taylor series coefficients of . is entire if is entire; so I hope it is.

Thanks for the encouragement Gottfried. Like all math; it's slow progress. Little breakthroughs from time to time.
Reply


Messages In This Thread
RE: holomorphic binary operators over naturals; generalized hyper operators - by JmsNxn - 08/10/2012, 10:57 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 135 09/09/2019, 10:38 PM
Last Post: tommy1729
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,552 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 625 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Hyper-volume by integration Xorter 0 1,219 04/08/2017, 01:52 PM
Last Post: Xorter
  Hyper operators in computability theory JmsNxn 5 3,429 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,328 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 35,315 09/02/2016, 02:11 AM
Last Post: tommy1729
  The bounded analytic semiHyper-operators JmsNxn 2 3,260 05/27/2016, 04:03 AM
Last Post: JmsNxn
  on constructing hyper operations for bases > eta JmsNxn 1 2,436 04/08/2015, 09:18 PM
Last Post: marraco
  Bounded Analytic Hyper operators JmsNxn 25 17,958 04/01/2015, 06:09 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)