Kneser's Super Logarithm
#5
(06/02/2009, 10:04 AM)Kouznetsov Wrote:
(06/02/2009, 09:24 AM)bo198214 Wrote:
(06/02/2009, 03:10 AM)Kouznetsov Wrote: About Kneser's expansion: it would be good to check, that we evaluate the same function expanding it at fixed point L and doing that at L^*....
Yes, there are singularities at the real axis at \( \exp^{[n]}(0) \). But thats only an intermediate step of Kneser's construction.
It is sufficient to show that the two expansions coincide along any segment of positive length. Then the two functions coincide in the whole range of the holomorphizm.

They dont coincide, because they are not real at the real axis.
Kneser's trick is to prepend a conformal mapping, that makes it real at the real axis.
Please have a look into my previous posts in this thread.


Moderator's note: I moved the two previous posts from thread overview paper co-author inviation to here.
Reply


Messages In This Thread
Kneser's Super Logarithm - by bo198214 - 11/19/2008, 02:20 PM
RE: Kneser's Super Logarithm - by bo198214 - 11/19/2008, 03:25 PM
RE: Kneser's Super Logarithm - by sheldonison - 01/23/2010, 01:01 PM
RE: Kneser's Super Logarithm - by mike3 - 01/25/2010, 06:35 AM
RE: Kneser's Super Logarithm - by sheldonison - 01/25/2010, 07:42 AM
RE: Kneser's Super Logarithm - by mike3 - 01/26/2010, 06:24 AM
RE: Kneser's Super Logarithm - by sheldonison - 01/26/2010, 01:22 PM
RE: Kneser's Super Logarithm - by mike3 - 01/27/2010, 06:28 PM
RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 08:30 PM
RE: Kneser's Super Logarithm - by mike3 - 01/28/2010, 08:52 PM
RE: Kneser's Super Logarithm - by sheldonison - 01/28/2010, 10:08 PM
RE: Kneser's Super Logarithm - by mike3 - 01/29/2010, 06:43 AM
RE: Kneser's Super Logarithm - by bo198214 - 01/26/2010, 11:19 PM
RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 07:51 PM
RE: Kneser's Super Logarithm - by bo198214 - 11/22/2008, 06:11 PM
RE: Kneser's Super Logarithm - by bo198214 - 11/23/2008, 01:00 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Artificial Neural Networks vs. Kneser Ember Edison 5 8,316 02/22/2023, 08:52 PM
Last Post: tommy1729
Question Derivative of the Tetration Logarithm Catullus 1 3,853 07/03/2022, 07:23 AM
Last Post: JmsNxn
  Complex to real tetration via Kneser Daniel 3 6,764 07/02/2022, 02:22 AM
Last Post: Daniel
Question Iterated Hyperbolic Sine and Iterated Natural Logarithm Catullus 2 5,625 06/11/2022, 11:58 AM
Last Post: tommy1729
  Trying to get Kneser from beta; the modular argument JmsNxn 2 5,361 03/29/2022, 06:34 AM
Last Post: JmsNxn
  Arguments for the beta method not being Kneser's method JmsNxn 54 86,373 10/23/2021, 03:13 AM
Last Post: sheldonison
  tommy's singularity theorem and connection to kneser and gaussian method tommy1729 2 6,506 09/20/2021, 04:29 AM
Last Post: JmsNxn
  Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 48,993 05/26/2021, 11:55 PM
Last Post: MphLee
  Alternative manners of expressing Kneser JmsNxn 1 5,472 03/19/2021, 01:02 AM
Last Post: JmsNxn
  Questions about Kneser... JmsNxn 2 7,444 02/16/2021, 12:46 AM
Last Post: JmsNxn



Users browsing this thread: 2 Guest(s)