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
  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)