imported>Dmitrii Kouznetsov |
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| {{Image notes
| | == Summary == |
| |Description= Analytic tetration <math>~G(z) </math> at base <math>b=\sqrt{2}</math>
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| on the complex <math>~z</math> plane,<br>
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| Solution of equation
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| <math>\exp_{\sqrt{2}}(G(z))=G(z+1)</math>
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| Levels of integer real part and those of integer imaginary part are shown with thick lines. Intermediate levels are shown with thin lines.
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| Grid covers with unit step range
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| (<math>-10\le \Re(z) \le 10 </math>,
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| <math>-10\le \Im(z) \le 10 </math>).
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| Function is periodic; period <math>T=17.1431~\rm i</math>.<br>
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| Asymptotic increment
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| <math> Q_1=\ln^2(2)\approx -0.36651292058166432701</math> at <math> \Re(z)\rightarrow \infty </math>, and
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| <math> Q_2=\ln^2(4)\approx 0.32663425997828098240</math> at <math> \Re(z)\rightarrow -\infty </math>.
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| Period: <math> T=\frac{2 \pi \rm i}{Q_2}\approx 19.23614904204285471 \!~ i </math>.
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| Asymptotic behavior:
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| : <math>G(z)\sim 4+{\rm e}^{Q_2z}+o({\rm e}^{Q_2z})</math>
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| |Author=Dmitrii Kouznetsov
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| |Date=2008
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| |Source=[[AnalyticTetrationBaseSqrt2u00/code]]
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| |Country first published in=Japan
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| |Copyright holder=Dmitrii Kouznetsov
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| |Notes=
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| |Other versions=}}
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| {{attribution}}
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