Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Taylor series of upx function
Kouznetsov Wrote:There is EXACT Tailor series, if we insist that upx(z^*) = upx(z)^*
and upx(z) is holomorphic outside the part of the negative part of axis,
id est, holomorphic everywhere except .
Then the solution is unique.
You can calculate so many derivatives as you like in any regular point, and, in particular, at z=0. The algorithm of evaluation is described in

Ok so far. My higher math skills aren't as good as I'd like them to be, so I'm not able to follow Dimitrii's paper. I'm looking at the pdf paper, and in section 2.1, Dimitrii writes:
Quote:(1.4) F(z + 1) = exp(F(z))
(2.1) ln(F(z + 1)) = F(z)
In this paper I assume that logarithm ln is single-valued function, that is analytic at the complex plane with cut along the negative part of the real axis. Then, all the solutions of equation (2.1) are solutions of (1.4), but it is not obvious, that a solution F of (1.4) satisfies also (2.1). One could add term 2i to the right hand side of equation (2.1), and the solution of the resulting equation will be also solution of (1.4). Searching for the simple tetration, I begin with analytic solutions, which satisfy also equation (2.1).
Shortly after thereafter, Dimitrii generates the value L for the critical point, but by then, I was already lost. I think the key is that in the complex plane, exp and ln, equations (1.4) and (2.1) are no longer inverses of each other, or perhaps more likely, that f(z) is an approximation function, which may not hold when adding increments of 2pi*i. Do you need the taylor series for f(z) to generate L? Is the key adding increments of 2*pi*i to the taylor series expansion for approximations of F(z)? Or does that require the contour integrals, in section (4)?
- Sheldon

Messages In This Thread
Taylor series of upx function - by Zagreus - 09/07/2008, 10:56 AM
RE: Taylor series of upx function - by bo198214 - 09/10/2008, 01:56 PM
RE: Taylor series of upx function - by andydude - 10/23/2008, 10:16 PM
RE: Taylor series of upx function - by Kouznetsov - 11/16/2008, 01:40 PM
RE: Taylor series of upx function - by bo198214 - 11/16/2008, 07:17 PM
RE: Taylor series of upx function - by Kouznetsov - 11/17/2008, 04:11 AM
RE: Taylor series of upx function - by bo198214 - 11/18/2008, 11:49 AM
RE: Taylor series of upx function - by sheldonison - 03/05/2009, 06:48 PM
RE: Taylor series of upx function - by Kouznetsov - 12/02/2008, 12:03 PM
RE: Taylor series of upx function - by Kouznetsov - 12/05/2008, 12:30 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 1,420 03/21/2020, 08:28 AM
Last Post: Daniel
  New mathematical object - hyperanalytic function arybnikov 4 1,928 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 912 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 1,357 10/22/2018, 11:29 AM
Last Post: Xorter
Question Taylor series of i[x] Xorter 12 15,123 02/20/2018, 09:55 PM
Last Post: Xorter
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 15,512 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,055 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,105 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 16,409 08/28/2016, 08:52 PM
Last Post: sheldonison
  Taylor polynomial. System of equations for the coefficients. marraco 17 20,204 08/23/2016, 11:25 AM
Last Post: Gottfried

Users browsing this thread: 1 Guest(s)