Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
base holomorphic tetration
#1
Hey folks,

until now we mainly considered holomorphy in the second argument of tetration:

.

If we now fix and demand also the function to be analytic on one small interval , the function is already determined for all other bases, particularly for bases by analytic continuation along the real axis (if there is no singularity at ).

For bases we know that the regular iteration at the lower fixed point is analytic there and continuable to 1.
So the question would be to what values the regular iteration continues for . I guess it has a branch point at and continues to complex values beyond .

I will explore this thought more concretely in the following posts.
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 7 875 08/14/2019, 09:15 AM
Last Post: sheldonison
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,313 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Is bounded tetration is analytic in the base argument? JmsNxn 0 1,134 01/02/2017, 06:38 AM
Last Post: JmsNxn
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 15,124 08/22/2016, 12:19 AM
Last Post: JmsNxn
  tetration base sqrt(e) tommy1729 2 3,019 02/14/2015, 12:36 AM
Last Post: tommy1729
  Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 2,659 02/13/2015, 02:26 PM
Last Post: Gottfried
  tetration base > exp(2/5) tommy1729 2 2,798 02/11/2015, 12:29 AM
Last Post: tommy1729
  regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 8,241 06/25/2013, 01:37 PM
Last Post: sheldonison
  tetration base conversion, and sexp/slog limit equations sheldonison 44 50,342 02/27/2013, 07:05 PM
Last Post: sheldonison
  simple base conversion formula for tetration JmsNxn 0 3,109 09/22/2011, 07:41 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)