Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Observations on power series involving logarithmic singularities
By the way, looking at it from this point of view helps make it clear why solving directly for the sexp was doomed to failure. You see, solving for the slog means composing F(z) with exp(z), to get F(exp(z)).

On the other hand, for a sexp function T, solving it would require the composition exp(T(z)). Exponentiating T necessarily means creating column vectors of powers of T, which means we are no longer dealing with a linear system.

And this is probably a general situation: finding G(F(x)), given the known power series for G and an unknown power series F, is going to lead to a non-linear system. However, F(G(x)) is still a linear system, because G is known.
~ Jay Daniel Fox

Messages In This Thread
RE: Observations on power series involving logarithmic singularities - by jaydfox - 11/05/2007, 07:42 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 1,547 02/18/2019, 10:34 PM
Last Post: Micah
Question Taylor series of i[x] Xorter 12 10,281 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,145 03/11/2017, 10:22 AM
Last Post: Xorter
  2 fixpoints related by power ? tommy1729 0 1,269 12/07/2016, 01:29 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 10,955 08/28/2016, 08:52 PM
Last Post: sheldonison
  Inverse power tower functions tommy1729 0 1,707 01/04/2016, 12:03 PM
Last Post: tommy1729
  Further observations on fractional calc solution to tetration JmsNxn 13 12,860 06/05/2014, 08:54 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,766 05/06/2014, 09:47 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 2,303 05/04/2014, 03:19 PM
Last Post: tommy1729
  about power towers and base change tommy1729 7 7,457 05/04/2014, 08:30 AM
Last Post: tommy1729

Users browsing this thread: 1 Guest(s)