A nice series for b^^h , base sqrt(2), by diagonalization
#20
(06/11/2009, 06:26 PM)Gottfried Wrote: Don't know yet, whether this has some benefit so far.

It looks, as if we had a discussion of that recently in Upper superexponential

I'm excerpting a bit of Henryk's post:
(03/29/2009, 11:23 AM)bo198214 Wrote: As it is well-known we have for the regular superexponential at the lower fixed point.

This can be obtained by computing the Schroeder function at the fixed point of .

(...)
Now the upper regular superexponential is the one obtained at the upper fixed point of .
For this function we have however always , so the condition can not be met.
Instead we normalize it by , which gives the formula:
(*1)
(...)

My construction in the previous post was obviously the same as that above construction (*1) ... Gottfried (I added the comments //... )

Gottfried Wrote:Then we can write

and the k'th coefficient in my first mail is just 2* C^k * d_k in the formula above.

where the fixpoint "a" is simply given as constant 2 and could be generalized to the symbol. The sum-expression describes the inverse of the schröder-function chi^-1 in Henryk's post. The formula for the repelling fixpoint replaces simply 2 by 4 and (1/2-1) by (5/4-1) and uses the adapted schröder-function. So I think it's useful to redirect replies to the other thread...
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: A nice series for b^^h , base sqrt(2), by diagonalization - by Gottfried - 06/11/2009, 08:36 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Kneser-iteration on n-periodic-points (base say \sqrt(2)) Gottfried 11 8,827 05/05/2021, 04:53 AM
Last Post: Gottfried
  Mathematica program for tetration based on the series with q-binomial coefficients Vladimir Reshetnikov 0 4,909 01/13/2017, 10:51 PM
Last Post: Vladimir Reshetnikov
  Expansion of base-e pentation andydude 13 44,004 07/02/2011, 01:40 AM
Last Post: Cherrina_Pixie
  Single-exp series computation code mike3 0 4,972 04/20/2010, 08:59 PM
Last Post: mike3
  Computations with the double-exp series mike3 0 4,340 04/20/2010, 07:32 PM
Last Post: mike3
  intuitive slog base sqrt(2) developed between 2 and 4 bo198214 1 6,682 09/10/2009, 06:47 PM
Last Post: bo198214
  sqrt(exp) Kouznetsov 15 33,270 12/20/2008, 01:25 PM
Last Post: Kouznetsov



Users browsing this thread: 1 Guest(s)