Thread Rating:
  • 1 Vote(s) - 1 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tetration extension for bases between 1 and eta
#6
(11/07/2009, 05:11 PM)bo198214 Wrote: But now there is still the question why the limit indeed satisfies
?

Actually it is not the case but we can obtain something very similar.
I just read in [1], p. 31, th. 10, that we have the following limit for a function
with :
for .

If we invert the formula we get


In our case though we dont have f(0)=0 but there is some fixed point of , .
In this case however the formula is quite similar, the only change is that .

[1] Ecalle: Theorie des invariants holomorphes
Reply


Messages In This Thread
RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 08:12 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Possible continuous extension of tetration to the reals Dasedes 0 1,140 10/10/2016, 04:57 AM
Last Post: Dasedes
  Andrew Robbins' Tetration Extension bo198214 32 39,686 08/22/2016, 04:19 PM
Last Post: Gottfried
  Why bases 0<a<1 don't get love on the forum? marraco 20 15,178 04/19/2015, 05:53 PM
Last Post: Gottfried
  Bundle equations for bases > 2 tommy1729 0 1,579 04/18/2015, 12:24 PM
Last Post: tommy1729
  on constructing hyper operations for bases > eta JmsNxn 1 2,408 04/08/2015, 09:18 PM
Last Post: marraco
  Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee 3 3,502 05/17/2014, 07:10 PM
Last Post: MphLee
  extension of the Ackermann function to operators less than addition JmsNxn 2 3,701 11/06/2011, 08:06 PM
Last Post: JmsNxn
  Alternate solution of tetration for "convergent" bases discovered mike3 12 16,820 09/15/2010, 02:18 AM
Last Post: mike3
  my accepted bases tommy1729 0 2,026 08/29/2010, 07:38 PM
Last Post: tommy1729
  [Regular tetration] bases arbitrarily near eta Gottfried 0 2,666 08/22/2010, 09:01 AM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)