Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Observations on power series involving logarithmic singularities
#15
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
Reply


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
  Perhaps a new series for log^0.5(x) Gottfried 3 878 03/21/2020, 08:28 AM
Last Post: Daniel
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 4,078 02/18/2019, 10:34 PM
Last Post: Micah
Question Taylor series of i[x] Xorter 12 13,767 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,563 03/11/2017, 10:22 AM
Last Post: Xorter
  2 fixpoints related by power ? tommy1729 0 1,712 12/07/2016, 01:29 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 14,872 08/28/2016, 08:52 PM
Last Post: sheldonison
  Inverse power tower functions tommy1729 0 2,076 01/04/2016, 12:03 PM
Last Post: tommy1729
  Further observations on fractional calc solution to tetration JmsNxn 13 15,504 06/05/2014, 08:54 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,807 05/06/2014, 09:47 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 2,856 05/04/2014, 03:19 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)