Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
elementary superfunctions
#23
(05/11/2009, 07:39 PM)bo198214 Wrote:
(05/11/2009, 05:17 PM)Ansus Wrote: It should be noted that superfunction is not unique in most cases. For example, for
, superfunction is

Ya, this is the simple kind of non-uniqueness, its just a translation along the x-axis.
However there are also more severe types of non-uniques, as I already introduced in my first post, we have two solutions (which are not translations of each other):
and .

1. Sorry, Henryk, they are translations of each other.
.
We already had similar discussion with respect to tetration on base ,
http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf , figure 3.
the growing up SuperExponential (red) and the tetration (blue), at the appropriate translations formula (5.7) and formula (5.Cool become very similar and bounded along the real axis functions (green). (I do not know why the number of forumla that follows (5.7) becomes some strange "smile". I mean just the number of formula, nothing more.)

2. There are many ways to extend the table of superfunctions.
I suggest the group of transforms of the pairs (TransferFunciton, SuperFunctions).

<b>Theorem</b>.
Let ,
Let ,
Let ,
Let .
Then .
Proof:

(end of proof).

With transform , from the pair (f,F) we get the pair (h,E).

2.1. Also, in the right hand side of the expression
we can swap and ;
this gives the new transfer function
with known superfunction .
Reply


Messages In This Thread
elementary superfunctions - by bo198214 - 04/23/2009, 01:25 PM
RE: elementary superfunctions - by bo198214 - 04/23/2009, 02:23 PM
RE: elementary superfunctions - by bo198214 - 04/23/2009, 03:46 PM
RE: elementary superfunctions - by tommy1729 - 04/27/2009, 11:16 PM
RE: elementary superfunctions - by bo198214 - 04/28/2009, 08:33 AM
RE: elementary superfunctions - by bo198214 - 03/27/2010, 10:27 PM
RE: elementary superfunctions - by bo198214 - 04/18/2010, 01:17 PM
RE: elementary superfunctions - by tommy1729 - 04/18/2010, 11:10 PM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 08:22 AM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 09:11 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 09:23 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 10:48 AM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 11:35 AM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 12:12 PM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 12:42 PM
RE: elementary superfunctions - by bo198214 - 04/25/2010, 01:10 PM
RE: elementary superfunctions - by Kouznetsov - 04/25/2010, 01:52 PM
Super-functions - by Kouznetsov - 05/11/2009, 02:02 PM
[split] open problems survey - by tommy1729 - 04/25/2010, 02:34 PM
RE: [split] open problems survey - by bo198214 - 04/25/2010, 05:15 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  I need somebody to help me clarifiy the elementary knowledge for tetration Ember Edison 13 1,290 08/26/2019, 01:44 PM
Last Post: Ember Edison
  Between exp^[h] and elementary growth tommy1729 0 1,021 09/04/2017, 11:12 PM
Last Post: tommy1729
  Superfunctions in continu sum equations tommy1729 0 1,864 01/03/2013, 12:02 AM
Last Post: tommy1729
  superfunctions of eta converge towards each other sheldonison 13 14,851 12/05/2012, 12:22 AM
Last Post: sheldonison
  how many superfunctions? [was superfunctions of eta converge towards each other] tommy1729 8 8,906 05/31/2011, 07:38 PM
Last Post: sheldonison
  Elliptic Superfunctions BenStandeven 2 3,754 08/20/2010, 11:56 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)