Thread Rating:
  • 1 Vote(s) - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Functional super-iteration and hierarchy of functional hyper-iterations
#19
(05/04/2009, 08:04 PM)Tetratophile Wrote: Your operator was defined with my operator. Here is the definition that you gave:

I gave a recursive definition, your operator is defined with my and my is defined with yours. They are defined simulataneously by the equations

(1) .
(2)
(3) and

Quote:Your I operator is basically the same as my It operator; the only differnce is the notation. Can you tell me exactly what is different about your definition of the hyper-
iteration rthan mine?

The difference is the declaration: Your operator It_n takes two functions and returns a function. My operator I_n takes a function and a number and returns a function.

Quote:[f It_n g](x) := [f It_n g(x)](x) - Let me clarify what it means.
Its absolutely clear what it means, however you see you make here the implicit distinction between It_n with a function as second argument (left side) and It_n with a number as second argument (right side).
To make the difference explicit rename It_n at the right side to I_n (and change the arrangement slightly). Then this exactly (1).

This equation can not be guessed! It needs to be written as part of the recursive definition!
Reply


Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/04/2009, 08:50 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 149 09/09/2019, 10:38 PM
Last Post: tommy1729
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 350 08/18/2019, 02:22 PM
Last Post: sheldonison
  Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 1,137 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,197 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,592 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse super-composition Xorter 11 11,427 05/26/2018, 12:00 AM
Last Post: Xorter
  Math overflow question on fractional exponential iterations sheldonison 4 3,068 04/01/2018, 03:09 AM
Last Post: JmsNxn
  The super 0th root and a new rule of tetration? Xorter 4 3,308 11/29/2017, 11:53 AM
Last Post: Xorter
  Hyper-volume by integration Xorter 0 1,221 04/08/2017, 01:52 PM
Last Post: Xorter
  Functional power Xorter 0 1,147 03/11/2017, 10:22 AM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)