Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Solving tetration for base 0 < b < e^-e
#15
(09/13/2009, 07:24 AM)mike3 Wrote: Why do you need to use a complex fixed point for ? It converges to a real fixed point as the tower approaches infinity (namely, ).

The problem with the real fixpoint is, that the triangular Bell-matrices have (alternating signed) units on its diagonal. This prevents the computation of a matrix-logarithm as well of the diagonalization - at least in my implementations.
If I have no option for one of those, I can approximate tetration only via diagonalization of the square Bell-matrices (means: omitting the fixpoint-shifting). But here all coefficients depend on the size of the used matrix, they are in my view unpredictable and may only serve as rough approximations for a "first impression".
But well, let's see. It's surely not the highest summit of wisdom... and we also have the Newton-binomial-formula and others...

Gottfried
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 2,986 08/14/2019, 09:15 AM
Last Post: sheldonison
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,558 01/02/2017, 06:38 AM
Last Post: JmsNxn
  Solving tetration using differintegrals and super-roots JmsNxn 0 2,123 08/22/2016, 10:07 PM
Last Post: JmsNxn
  tetration base sqrt(e) tommy1729 2 3,668 02/14/2015, 12:36 AM
Last Post: tommy1729
  Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 3,270 02/13/2015, 02:26 PM
Last Post: Gottfried
  tetration base > exp(2/5) tommy1729 2 3,439 02/11/2015, 12:29 AM
Last Post: tommy1729
  regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,103 06/25/2013, 01:37 PM
Last Post: sheldonison
  tetration base conversion, and sexp/slog limit equations sheldonison 44 60,175 02/27/2013, 07:05 PM
Last Post: sheldonison
  simple base conversion formula for tetration JmsNxn 0 3,485 09/22/2011, 07:41 PM
Last Post: JmsNxn
  Does anyone have taylor series approximations for tetration and slog base e^(1/e)? JmsNxn 18 22,868 06/05/2011, 08:47 PM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)