Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
A functional equation
#1
Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks

Reply
#2

Let's start there. Then, we plug in 1 to get . Then .
Reply
#3
(07/05/2010, 07:28 PM)kobi_78 Wrote: Hi,

Does anyone have an idea how to solve the following functional equation?

Thanks


Thats called "Julia equation", generally
f(F(x))=F'(x)f(x) to solve for f.

You obtain an Abel function from it, or obtain it from an Abel function via:


you can solve it at a fixed point via comparing the powerseries coefficients.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Modding out functional relationships; An introduction to congruent integration. JmsNxn 3 869 06/23/2021, 07:07 AM
Last Post: JmsNxn
  [MSE] Help on a special kind of functional equation. MphLee 4 944 06/14/2021, 09:52 PM
Last Post: JmsNxn
  Moving between Abel's and Schroeder's Functional Equations Daniel 1 3,014 01/16/2020, 10:08 PM
Last Post: sheldonison
Big Grin Logical tetration equation Xorter 0 2,933 02/01/2018, 10:29 PM
Last Post: Xorter
  Functional power Xorter 0 2,896 03/11/2017, 10:22 AM
Last Post: Xorter
  Some sort equation ... tommy1729 0 2,957 10/15/2015, 12:12 PM
Last Post: tommy1729
  An intresting equation ? Taking squares by equation. tommy1729 0 3,112 05/08/2015, 11:37 PM
Last Post: tommy1729
  Conservation of functional equation ? tommy1729 0 3,094 05/01/2015, 10:03 PM
Last Post: tommy1729
  Is this THE equation for parabolic fix ? tommy1729 5 11,124 04/16/2015, 10:01 PM
Last Post: tommy1729
  Mick's differential equation tommy1729 3 6,338 04/10/2015, 04:14 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)