File:AnalyticTetrationBaseSqrt2v00.jpg: Difference between revisions
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{{Image notes | {{Image notes | ||
|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. | on the complex <math>~z</math> plane.<br> | ||
Levels of integer real part and those of integer imaginary part are shown with thick lines. | 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 | Grid covers with unit step range | ||
<math>-10\le \Re(z) \le 10 </math> | (<math>-10\le \Re(z) \le 10 </math>, | ||
<math>-10\le \Im(z) \le 10 </math>. | <math>-10\le \Im(z) \le 10 </math>). | ||
Function is periodic; period <math>T=17.1431~\rm i</math>. | Function is periodic; period <math>T=17.1431~\rm i</math>.<br> | ||
Asumptotic increment | Asumptotic increment | ||
<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 | ||
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