Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
base holomorphic tetration
#36
(11/16/2009, 09:01 AM)bo198214 Wrote: Mike, I took the extra time to describe it in my previous post:
(11/16/2009, 12:30 AM)bo198214 Wrote: I computed the regular iteration as a mixture of the powerseries development at the lower fixed point, together with (if 1 is not inside the convergence radius of this powerseries) the equality , i.e. the exponentials move the argument towards the fixed point until it is inside its convergence radius then the powerseries can be applied and the same number of logarithms have to finish the computation.

I assumed the convergence radius to be at least the distance of the fixed point from the image of the Shell-Thron region.

Ah, I see now. How much numerical precision was required, though?

Quote:What about the vicinity of the area ?
In which form/region you want it to be shown? Different sectors, or decreasing distance to the boundary?

Region? I suppose a small circle around e^{1/e}, excluding the wedge that lies outside the STR?
Reply


Messages In This Thread
base holomorphic tetration - by bo198214 - 11/05/2009, 02:12 PM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 04:15 AM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 11:58 AM
RE: base holomorphic tetration - by bo198214 - 11/06/2009, 12:12 PM
RE: base holomorphic tetration - by mike3 - 11/06/2009, 09:16 PM
RE: base holomorphic tetration - by bo198214 - 11/06/2009, 11:29 PM
RE: base holomorphic tetration - by mike3 - 11/07/2009, 12:23 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 08:17 AM
RE: base holomorphic tetration - by mike3 - 11/07/2009, 08:21 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 09:55 AM
RE: base holomorphic tetration - by bo198214 - 11/07/2009, 04:47 PM
RE: base holomorphic tetration - by bo198214 - 11/08/2009, 05:39 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:27 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:25 PM
RE: base holomorphic tetration - by bo198214 - 11/08/2009, 08:44 PM
RE: base holomorphic tetration - by mike3 - 11/08/2009, 09:51 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 3,324 08/14/2019, 09:15 AM
Last Post: sheldonison
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 5,274 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,620 01/02/2017, 06:38 AM
Last Post: JmsNxn
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 18,405 08/22/2016, 12:19 AM
Last Post: JmsNxn
  tetration base sqrt(e) tommy1729 2 3,788 02/14/2015, 12:36 AM
Last Post: tommy1729
  Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 3,376 02/13/2015, 02:26 PM
Last Post: Gottfried
  tetration base > exp(2/5) tommy1729 2 3,561 02/11/2015, 12:29 AM
Last Post: tommy1729
  regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,403 06/25/2013, 01:37 PM
Last Post: sheldonison
  tetration base conversion, and sexp/slog limit equations sheldonison 44 61,561 02/27/2013, 07:05 PM
Last Post: sheldonison
  simple base conversion formula for tetration JmsNxn 0 3,542 09/22/2011, 07:41 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)