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...)
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{{Image notes
== Summary ==
|Description= Analytic tetration <math>~F(z) </math> at base <math>b=\sqrt{2}</math>
Importing file
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) \le 10 </math>).
Function is periodic; period <math>T=17.1431~\rm i</math>.<br>
 
Asumptotic increment
<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>.
|Author=Dmitrii Kouznetsov
|Date=2008
|Source=[[AnalyticTetrationBaseSqrt2v00/code]]
|Country first published in=Japan
|Copyright holder=Dmitrii Kouznetsov
|Notes=
|Other versions=}}
{{attribution}}

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