Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Taylor polynomial. System of equations for the coefficients.
#11
(05/05/2015, 07:40 AM)Gottfried Wrote: P*A = A*Bb

I think that we are speaking of different things.

Obviously, there should be a way to demonstrate the equivalence of both, because they are trying to solve the same problem; looking for the same solution.

But as I understand, the Carleman matrix A only contains powers of a_i coefficients, yet if you look at the red side, it cannot be written as a matrix product A*Bb, because it needs to have products of a_i coefficients (like ). Maybe it is a power of A.Bb, or something like A^Bb?

The Pascal matrix on the blue side is the exponential of a much simpler matrix



Maybe the equation can be greatly simplified by taking a logarithm of both sides.
I have the result, but I do not yet know how to get it.
Reply


Messages In This Thread
RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/06/2015, 02:42 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
Question Taylor series of i[x] Xorter 12 10,103 02/20/2018, 09:55 PM
Last Post: Xorter
  Taylor series of cheta Xorter 13 10,782 08/28/2016, 08:52 PM
Last Post: sheldonison
  Totient equations tommy1729 0 1,576 05/08/2015, 11:20 PM
Last Post: tommy1729
  Bundle equations for bases > 2 tommy1729 0 1,576 04/18/2015, 12:24 PM
Last Post: tommy1729
  Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 1,873 01/03/2015, 11:02 PM
Last Post: MphLee
  A system of functional equations for slog(x) ? tommy1729 3 4,031 07/28/2014, 09:16 PM
Last Post: tommy1729
  partial invariant equations ? tommy1729 0 1,680 03/16/2013, 12:32 AM
Last Post: tommy1729
  tetration base conversion, and sexp/slog limit equations sheldonison 44 50,405 02/27/2013, 07:05 PM
Last Post: sheldonison
  Superfunctions in continu sum equations tommy1729 0 1,839 01/03/2013, 12:02 AM
Last Post: tommy1729
  Can we prove these coefficients must be constant? JmsNxn 0 1,743 06/03/2012, 09:17 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)