Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Simplified regular tetration
#2
We know that we can express the Abel function of at by
where is the Schröder function of at , where .
This means that the inverse of the Abel function which is actually the superexponential can be expressed by
with appropriate translation along the x-axis choosen such that . Here

The coefficients of , , , can be recursively computed from the equation
(*) ,
by the composition formula
where .

Now we put formula (*) in:

On the right side only occurs for in , namely in the summand . Thatswhy we have the recursive formula:


So each coefficient of is a polynomial in ( base) and a rational function in ( fixed point).
and upto translation along the x-Axis we have .
Reply


Messages In This Thread
Simplified regular tetration - by andydude - 05/02/2009, 12:13 AM
RE: Simplified regular tetration - by bo198214 - 05/02/2009, 08:47 AM
RE: Simplified regular tetration - by andydude - 05/03/2009, 08:49 AM
RE: Simplified regular tetration - by bo198214 - 05/03/2009, 09:33 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Regular iteration using matrix-Jordan-form Gottfried 7 9,320 09/29/2014, 11:39 PM
Last Post: Gottfried
  regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,103 06/25/2013, 01:37 PM
Last Post: sheldonison
  regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) JmsNxn 5 8,035 06/15/2011, 12:27 PM
Last Post: Gottfried
  Regular "pentation"? mike3 12 22,017 04/04/2011, 03:16 AM
Last Post: BenStandeven
  closed form for regular superfunction expressed as a periodic function sheldonison 31 34,163 09/09/2010, 10:18 PM
Last Post: tommy1729
  [Regular tetration] [Iteration series] norming fixpoint-dependencies Gottfried 11 14,552 08/31/2010, 11:55 PM
Last Post: tommy1729
  regular tetration at b=e^(-e) bo198214 6 10,448 08/23/2010, 05:45 PM
Last Post: Gottfried
  [Regular tetration] bases arbitrarily near eta Gottfried 0 2,972 08/22/2010, 09:01 AM
Last Post: Gottfried
  "Natural boundary", regular tetration, and Abel matrix mike3 9 15,801 06/24/2010, 07:19 AM
Last Post: Gottfried
  Regular slog for base sqrt(2) - Using z=2 jaydfox 13 19,500 03/10/2010, 12:47 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)