Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
closed form for regular superfunction expressed as a periodic function
#29
(09/07/2010, 07:46 PM)tommy1729 Wrote: it only has a formal powerseries that converges at the integers but has radius 0 hence not analytic.

Ya but it is analytic outside the fixed point. There is one half-iterate to the right of the fixed point and one to the left, which are different functions, i.e. no analytic continuations of each other. Both iterates have the asymptotic power series expansion at the fixed point that one gets when calculating the *formal* powerseries (which has 0 convergence radius).


Reply


Messages In This Thread
RE: closed form for regular superfunction expressed as a periodic function - by bo198214 - 09/08/2010, 06:03 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 141 09/09/2019, 10:55 PM
Last Post: tommy1729
  Is there a function space for tetration? Chenjesu 0 245 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 720 10/22/2018, 11:29 AM
Last Post: Xorter
  Periodic analytic iterations by Riemann mapping tommy1729 1 2,034 03/05/2016, 10:07 PM
Last Post: tommy1729
  Should tetration be a multivalued function? marraco 17 15,312 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 3,321 01/10/2016, 06:14 PM
Last Post: tommy1729
  Natural cyclic superfunction tommy1729 3 2,761 12/08/2015, 12:09 AM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 1,817 04/21/2015, 01:02 PM
Last Post: tommy1729
  Can sexp(z) be periodic ?? tommy1729 2 3,582 01/14/2015, 01:19 PM
Last Post: tommy1729
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,804 11/09/2014, 10:20 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)