Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
A relaxed [tex]\zeta[/tex]-extensions of the Recursive Hyperoperations
A relaxed -extensions of the Recursive Hyperoperations

I want to show you an easy extension for hyperoperations.
I don't want it to be the most natural, but I want to ask if someone already used this extension and if it can be usefull for something.

Since is a bit different I want to use the plus-notation () for the hyperoperators.

I start with these basic definitions over the naturals :

Then the recursive definitions of the operators

Observation before the extension's definitons

we can see that from rank zero to rank one we can define infinite functions with

Generalizing, now we can define as a continous functions from the interval to , to the interval to :

And we can define the operations with fractional rank starting from the interval

Other operations are these ( and ):

Example of functions and the generated -hyperoperations:


for and
MathStackExchange account:MphLee

Possibly Related Threads...
Thread Author Replies Views Last Post
  There is a non recursive formula for T(x,k)? marraco 5 1,444 12/26/2020, 11:05 AM
Last Post: Gottfried
  Recursive formula generating bounded hyper-operators JmsNxn 0 2,684 01/17/2017, 05:10 AM
Last Post: JmsNxn
  @Andydude References about the formalization of the Hyperoperations MphLee 3 6,038 07/25/2014, 10:41 AM
Last Post: MphLee
  Easy tutorial on hyperoperations and noptiles MikeSmith 2 4,637 06/26/2014, 11:58 PM
Last Post: MikeSmith
  Negative, Fractional, and Complex Hyperoperations KingDevyn 2 8,952 05/30/2014, 08:19 AM
Last Post: MphLee
  Zeta iterations Balarka Sen 11 17,618 02/26/2013, 09:49 AM
Last Post: Gottfried
  Non-recursive coefficient formulas. Can the Riemann mapping be constructed? mike3 0 3,220 06/04/2011, 12:17 AM
Last Post: mike3
  zeta and sinh tommy1729 0 2,953 05/30/2011, 12:07 PM
Last Post: tommy1729
  Generalized recursive operators Whiteknox 39 56,780 04/04/2011, 11:52 PM
Last Post: Stan

Users browsing this thread: 1 Guest(s)