File:AnalyticTetrationBaseSqrt2v00.jpg: Difference between revisions

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imported>Dmitrii Kouznetsov
(uploaded a new version of "Image:AnalyticTetrationBaseSqrt2v00.jpg": {{Image notes |Description= Analytic tetration <math>~F(z) </math> at base <math>b=\sqrt{2}</math> on the complex <math>~z</math> plane.<br> Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines. <math>F(-1)=0</math>, <math>F(0)=1</math>. <br> Grid covers with unit step range (<math>-10\le \Re(z) \le 10 </math>, <math>-10\le \Im(z) \l...)
imported>Caesar Schinas
m (Bot: Replace Template:Image_notes_* with Template:Image_Details)
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{{Image notes
{{Image_Details
|Description= Analytic tetration <math>~F(z) </math> at base <math>b=\sqrt{2}</math>
|description  = Analytic tetration <math>~F(z) </math> at base <math>b=\sqrt{2}</math>
on the complex <math>~z</math> plane.<br>
on the complex <math>~z</math> plane.<br>
Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines.  
Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines.  
Line 14: Line 14:
<math> Q=\ln^2(2)\approx -0.366513</math> at  <math> \Re(z)\rightarrow \infty </math>,  and
<math> Q=\ln^2(2)\approx -0.366513</math> at  <math> \Re(z)\rightarrow \infty </math>,  and
<math> Q=\ln^2(4)\approx 0.3266342</math> at  <math> \Re(z)\rightarrow -\infty </math>.
<math> Q=\ln^2(4)\approx 0.3266342</math> at  <math> \Re(z)\rightarrow -\infty </math>.
|Author=Dmitrii Kouznetsov
|author      = Dmitrii Kouznetsov
|Date=2008
|copyright    = Dmitrii Kouznetsov
|Source=[[AnalyticTetrationBaseSqrt2v00/code]]
|source      = [[AnalyticTetrationBaseSqrt2v00/code]]
|Country first published in=Japan
|date-created = 2008
|Copyright holder=Dmitrii Kouznetsov
|pub-country  = Japan
|Notes=
|notes        =  
|Other versions=}}  
|versions     =  
}}  
{{attribution}}
{{attribution}}

Revision as of 04:35, 22 June 2009

Title / Description


Analytic tetration at base

on the complex plane.
Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines.

, .

Grid covers with unit step range (, ). Function is periodic; period .

Asumptotic increment at , and at .

Author(s)


Dmitrii Kouznetsov
Copyright holder


Dmitrii Kouznetsov
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Source


AnalyticTetrationBaseSqrt2v00/code
Date created


2008
Country of first publication


Japan
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