Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Non-recursive coefficient formulas. Can the Riemann mapping be constructed?
#1
Hi.

Here:

http://math.eretrandre.org/tetrationforu...49#pid5749

I gave an explicit, non-recursive coefficient formula for the coefficients of the regular Schroder function of :


.

(the curly-brackets thing is a Stirling number of the 2nd kind)

This is in a very "general" form -- e.g. the Bernoulli numbers can also be written in a form similar to this (as in the thread, I mention how it comes from a solution of a general kind of recurrence equation.). I wonder if this can be "specialized" to yield a more interesting formula, like how the Bernoulli numbers can be written as a double-sum.

Note that this formula requires exponentially increasing numbers of terms, which makes it not suitable for computation (recurrence is best). But I'm more curious about its use for doing analysis of the generated function. Could this be used somehow to help get the coefficients of the Riemann mapping to build the full tetrational at, say, base ? Perhaps it can be simplified to one with less terms. Any thoughts?
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,293 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Periodic analytic iterations by Riemann mapping tommy1729 1 1,917 03/05/2016, 10:07 PM
Last Post: tommy1729
  [split] Understanding Kneser Riemann method andydude 7 6,958 01/13/2016, 10:58 PM
Last Post: sheldonison
  [MO] something practical on Riemann-mapping Gottfried 0 1,699 01/05/2015, 02:33 PM
Last Post: Gottfried
  Riemann surface equation RB ( f(z) ) = f( p(z) ) tommy1729 1 2,100 05/29/2014, 07:22 PM
Last Post: tommy1729
  A relaxed [tex]\zeta[/tex]-extensions of the Recursive Hyperoperations MphLee 0 1,728 06/14/2013, 09:57 PM
Last Post: MphLee
  theta and the Riemann mapping sheldonison 2 5,008 10/11/2011, 12:49 PM
Last Post: sheldonison
  Generalized recursive operators Whiteknox 39 38,486 04/04/2011, 11:52 PM
Last Post: Stan
  coefficient of polynomial (x+1)(x+2)(x+3)...(x+n) dev 1 3,060 02/13/2011, 06:48 PM
Last Post: bo198214
  "Kneser"-like mapping also for complex base? mike3 2 5,408 11/07/2010, 01:37 PM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)