Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
weird series expansion
#1
consider F(x) a real-analytic function mapping R+ to R+ with only a single fixpoint, the one at 0.

let g(x,n) be g(g(x,n-1),1) and g(x,1) = arcsinh(x/2)

F(x) is strictly nondecreasing. F(x) grows slower than x^2 + 1.

let a_n be real.

the following weird series expansion has come to my mind :

a0 + a1 x + a2 g(x,1) + a3 g(x,2) + a4 g(x,3) + ...

and many questions pop up.

regards

tommy1729
Reply
#2
g(x,n) = g(g(x,n-1))
The right side of the equation uses g as a function on one variable. How is g(x) defined?
Reply
#3
i corrected it ... should be clear now.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
Question Taylor series of i[x] Xorter 12 10,271 02/20/2018, 09:55 PM
Last Post: Xorter
  Taylor series of cheta Xorter 13 10,945 08/28/2016, 08:52 PM
Last Post: sheldonison
  [integral] How to integrate a fourier series ? tommy1729 1 2,301 05/04/2014, 03:19 PM
Last Post: tommy1729
  Iteration series: Series of powertowers - "T- geometric series" Gottfried 10 15,656 02/04/2012, 05:02 AM
Last Post: Kouznetsov
  Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 2,669 09/04/2011, 05:59 AM
Last Post: Gottfried
  What is the convergence radius of this power series? JmsNxn 9 14,845 07/04/2011, 09:08 PM
Last Post: JmsNxn
  An alternate power series representation for ln(x) JmsNxn 7 12,913 05/09/2011, 01:02 AM
Last Post: JmsNxn
  Something interesting about Taylor series Ztolk 3 6,069 06/29/2010, 06:32 AM
Last Post: bo198214
  Transseries, nest-series, and other exotic series representations for tetration mike3 26 28,384 12/15/2009, 01:00 PM
Last Post: bo198214
  Tetra-series Gottfried 29 28,999 11/03/2009, 05:04 AM
Last Post: andydude



Users browsing this thread: 1 Guest(s)