New mathematical object - hyperanalytic function

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New mathematical object - hyperanalytic function

Daniel $Offline$
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01/02/2020, 12:15 AM

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

has approximation

$A\left( x \right)=\frac{\mathbb{R}_{max}+\mathbb{R}_{min}}{2}(1+2\alpha cos(2\pi x )$

{Please fix, doesn't parse}
$+2\sum_{i=1}^{\infty} \alpha^{4^i}( \cos ( 2i \times 2\pi x ) -1 )<br /> +\frac{2}{\mathbb{W}_{max}}\sum_{i=1}^{\infty}\alpha^{9{i}^2}\left( cos\left(3 \times (2i-1)\times 2\pi x \right)<br /> -cos\left( (2i-1) \times 2\pi x \right) \right)$ ,

where

$\alpha\left(\sigma\right)=\frac{1}{2}\frac{\mathbb{R}_{max}-\mathbb{R}_{min}}{\mathbb{R}_{max}+\mathbb{R}_{min}}$ .

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Messages In This Thread

New mathematical object - hyperanalytic function - by arybnikov - 12/30/2019, 04:18 PM

RE: New mathematical object - hyperanalytic function - by bo198214 - 12/31/2019, 11:04 PM

RE: New mathematical object - hyperanalytic function - by arybnikov - 01/01/2020, 10:51 PM

RE: New mathematical object - hyperanalytic function - by Daniel - 01/02/2020, 12:15 AM

RE: New mathematical object - hyperanalytic function - by arybnikov - 01/02/2020, 01:38 AM

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