File:TetrationPolynomial25power.jpg

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Title / Description	Approimation of holomorphic tetration with polynomial of 25th power, id est, the partial sum of the Tailor series. In the uper right corner, the $f=\sum _{n=0}^{25}c_{n}z^{n}$ is plotted with lines of constant real part and constant imaginary part in the complex [tex]z[/tex] plane. Levels $\Re (f)=-2,-1,0,1,2,3,4$ are shown with thick black curves. Levels $\Re (f)=-1.8,-1.6,-1.4,-1.2,-0.8,-0.6,-0.4,-0.2$ are shown with thin red curves. Levels $\Re (f)=1.8,1.6,1.4,1.2,0.8,0.6,0.4,0.2$ are shown with thin thin blue curves. Levels $\Im (f)=-2,-1$ are shown with thick red curves. Levels $\Im (f)=1,2$ are shown with thick blue curves. Levels $\Im (f)=\pm \pi ,\pm 3\pi$ are shown with thick pink curves. Levels $\Im (f)=\pm 1.8,\pm 1.6,\pm 1.4,\pm 1.2,\pm 0.8,\pm 0.6,\pm 0.4,\pm 0.2$ are shown with thin green curves.
Author(s)	Dmitrii Kouznetsov
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Date created	2008
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