Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
New mathematical object - hyperanalytic function
#1
New mathematical object - hyperanalytic function is introduced. The convergence of hyperanalytic functions is substantially above than the convergence of analytic functions. A specific sample of hyperanalytic function is the reticulum function (RF). This function describes the reticulum space-time. RF can't be decomposed into the Fourier series and, therefore, RF does not provide the conservation of parity as the analytic functions do. Thanks to this, the RF can be decomposed in an endless series of two primitive hyperanalytic functions by sequential attempts of decomposition in the even and odd functions. The unique parameter of such series is the fine structure constant.
It allows combine all fundamental interactions into the Naturally-Unified Quantum Theory of Interactions. The price of such quantum unification is the reticulum space-time.

Additional material: http://www.gaussianfunction.com
Reply
#2
How is this related to tetration?
Reply
#3
(12/31/2019, 11:04 PM)bo198214 Wrote: How is this related to tetration?

Directly.
For example, function

Code:
\mathbb{R}(x)=\frac{1}{\sigma\sqrt{2\pi}}\sum_{n=-\infty}^{\infty}e^{-\frac{1}{2}(\frac{x-nL}{\sigma})^{2}}

has approximation

Code:
A\left(x\right)=\frac{\mathbb{R}_{max}+\mathbb{R}_{min}}{2}(1+2\alpha cos\left(2\pi x\right))
+2\sum_{i=1}^{\infty}\alpha^{4^{i}}\left(cos\left(2i\times 2\pi x\right)-1\right)+\frac{2}{\mathbb{W}_{max}}\sum_{i=1}^{\infty}\alpha^{9{i}^2}\left(cos\left(3 \times (2i-1)\times 2\pi x\right)-cos\left((2i-1) \times 2\pi  x\right)\right),

where

Code:
\alpha\left(\sigma\right)=\frac{1}{2}\frac{\mathbb{R}_{max}-\mathbb{R}_{min}}{\mathbb{R}_{max}+\mathbb{R}_{min}}.
Reply
#4
(01/01/2020, 10:51 PM)arybnikov Wrote:
(12/31/2019, 11:04 PM)bo198214 Wrote: How is this related to tetration?

Directly.
For example, function


has approximation



{Please fix, doesn't parse}
,

where

.
Daniel
Reply
#5
(01/02/2020, 12:15 AM)Daniel Wrote:
(01/01/2020, 10:51 PM)arybnikov Wrote:
(12/31/2019, 11:04 PM)bo198214 Wrote: How is this related to tetration?

Directly.
For example, function


has approximation



,

where

.

Unfortunately I still have problem with  and [?].
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  Fibonacci as iteration of fractional linear function bo198214 48 2,199 09/14/2022, 08:05 AM
Last Post: Gottfried
  Constructing an analytic repelling Abel function JmsNxn 0 208 07/11/2022, 10:30 PM
Last Post: JmsNxn
  A related discussion on interpolation: factorial and gamma-function Gottfried 9 18,182 07/10/2022, 06:23 AM
Last Post: Gottfried
  A Holomorphic Function Asymptotic to Tetration JmsNxn 2 1,916 03/24/2021, 09:58 PM
Last Post: JmsNxn
  Is there a function space for tetration? Chenjesu 0 2,645 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 3,104 10/22/2018, 11:29 AM
Last Post: Xorter
  Should tetration be a multivalued function? marraco 17 35,211 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 7,797 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 3,988 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 12,994 05/13/2014, 02:18 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)