File:AnalyticTetrationBaseSqrt2v00.jpg

${\displaystyle ~F(z)}$

${\displaystyle b={\sqrt {2}}}$

on the complex ${\displaystyle ~z}$ plane.
Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines.

${\displaystyle F(-1)=0}$, ${\displaystyle F(0)=1}$.

Grid covers with unit step range (${\displaystyle -10\leq \Re (z)\leq 10}$, ${\displaystyle -10\leq \Im (z)\leq 10}$). Function is periodic; period ${\displaystyle T=17.1431~{\rm {i}}}$.

Asumptotic increment ${\displaystyle Q=\ln ^{2}(2)\approx -0.366513}$ at ${\displaystyle \Re (z)\rightarrow \infty }$, and ${\displaystyle Q=\ln ^{2}(4)\approx 0.3266342}$ at ${\displaystyle \Re (z)\rightarrow -\infty }$.

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