Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Infinite tetration and superroot of infinitesimal
Hey Gianfranco,

open your eyes! Catastrophe theory will not solve your problems with multivalued functions, nor will the use of the term "multivalued function".
I think I clarified in detail what terms are there and how to use them:
1. There is an analytic function (single valued)
2. If the function has only isolated singularities choose slices starting at the singularities for extending this function (uniquely/single valued) to the sliced complex plane.
3. Determine branches of the function by paths that cross the slices.

If your original analytic function is not injective, you can invert it at a point with . That means there is a unique inversion in a neighborhood of . If you look at the branches of you will find among them also the other values for which , i.e. for each with there will be a branch such that . Or in other words for each there is a such that .

For example the function (sliced as usual) has the branches , i.e. at all only 2 branches that is and . And hence is not always equal to but we have to choose the right branch for example and . In general we have merely . And no multivalued function consideration will save you from considering this.
Reply


Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by bo198214 - 02/01/2008, 09:29 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 885 03/20/2018, 12:16 AM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 10,584 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,590 05/06/2014, 09:47 PM
Last Post: tommy1729
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 6,142 07/17/2013, 09:46 AM
Last Post: Gottfried
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,024 09/06/2012, 02:01 AM
Last Post: JmsNxn
  the infinite operator, is there any research into this? JmsNxn 2 5,034 07/15/2011, 02:23 AM
Last Post: JmsNxn
  Infinite tetration of the imaginary unit GFR 40 49,186 06/26/2011, 08:06 AM
Last Post: bo198214
  Infinite Pentation (and x-srt-x) andydude 20 23,778 05/31/2011, 10:29 PM
Last Post: bo198214
  Infinite tetration fractal pictures bo198214 15 21,019 07/02/2010, 07:22 AM
Last Post: bo198214
  Infinite towers & solutions to Lambert W-function brangelito 1 3,458 06/16/2010, 02:50 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)