Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Should tetration be a multivalued function?
#5
(01/04/2016, 12:01 AM)andydude Wrote: It appears that these 3 branches are not connected in the real line, but I would suspect that they are connected in the complex plane (to make a Riemann surface), and that fixing on the main branch might fix the value of the other branches, at least that's what I would think.
[Note: the asymptotes make 5 branches]

If the transition is not singular, then the blue branch should be coincident with the black (main) branch for . That may give a clue about his better value for °a.

[Edit: the transition for the blue branch must be singular, because it cannot smoothly change from an horizontal asymptote to a parallel line to the main branch, which has a vertical asymptote.
That unless tetration introduces a new kind of numbers which are continuous in the transition.]

They should be coincident, because for the blue branch, any value chosen for °a, is also somewhere in the main branch, so taking iterated logarithms/exponentiations should give the same result.
I have the result, but I do not yet know how to get it.
Reply


Messages In This Thread
RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 12:08 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 363 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 500 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 949 10/22/2018, 11:29 AM
Last Post: Xorter
  Introducing new special function : Lambert_t(z,r) tommy1729 2 3,729 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 2,017 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 7,746 05/13/2014, 02:18 PM
Last Post: JmsNxn
  entire function close to sexp ?? tommy1729 8 9,727 04/30/2014, 03:49 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,050 07/17/2013, 09:46 AM
Last Post: Gottfried
  Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 3,100 06/15/2013, 08:02 PM
Last Post: MphLee
  Hyperzeta function Balarka Sen 7 8,146 05/08/2013, 01:36 PM
Last Post: Balarka Sen



Users browsing this thread: 1 Guest(s)