Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Applying the iteration methods to simpler functions
#8
You are confusing Bell matrices and Carleman matrices again. The (generalized) Bell matrix of is

whereas the Carleman matrix (is

all the other stuff is right, though, and interesting. I like your notation, but I'm having trouble following your series notation.

I think the example of is an interesting one, and I intend on looking into it, but first for the purposes of illustration, your simplest example is the nicest, for example, addition . Taking the Bell matrix:

and subtracting the identity matrix:

gives a non-invertible matrix, so doing the choppy thing gives:

putting this in the matrix equation gives:

and since the matrix is invertible now, we can multiply both sides by its inverse:

This gives the natural Abel function (choosing the constant term to be zero) which satisfies the equation .

I like that example Smile I know you already talked about it, but I wanted to show a matrix-based way of doing the chopping process.

So in general, the matrix equation would give the coefficients of the natural Abel function of f.

Andrew Robbins
Reply


Messages In This Thread
RE: Applying the iteration methods to simpler functions - by andydude - 11/12/2007, 09:40 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  The AB functions ! tommy1729 0 1,659 04/04/2017, 11:00 PM
Last Post: tommy1729
  the inverse ackerman functions JmsNxn 3 6,160 09/18/2016, 11:02 AM
Last Post: Xorter
  Look-alike functions. tommy1729 1 2,143 03/08/2016, 07:10 PM
Last Post: hixidom
  Inverse power tower functions tommy1729 0 1,964 01/04/2016, 12:03 PM
Last Post: tommy1729
  [2014] composition of 3 functions. tommy1729 0 1,861 08/25/2014, 12:08 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 2,611 05/22/2014, 04:56 PM
Last Post: sheldonison
  Intresting functions not ? tommy1729 4 5,338 03/05/2014, 06:49 PM
Last Post: razrushil
  [Update] Comparision of 5 methods of interpolation to continuous tetration Gottfried 30 30,856 02/04/2014, 12:31 AM
Last Post: Gottfried
  applying continuum sum to interpolate any sequence. JmsNxn 1 2,996 08/18/2013, 08:55 PM
Last Post: tommy1729
  generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 22,908 11/24/2011, 01:18 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)