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-rw-r--r-- | buch/chapters/080-funktionentheorie/images/fortsetzreziprok.tex | 65 |
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diff --git a/buch/chapters/080-funktionentheorie/images/fortsetzreziprok.tex b/buch/chapters/080-funktionentheorie/images/fortsetzreziprok.tex new file mode 100644 index 0000000..4fa4a68 --- /dev/null +++ b/buch/chapters/080-funktionentheorie/images/fortsetzreziprok.tex @@ -0,0 +1,65 @@ +% +% fortsetzreziprok.tex -- analytische Fortsetzung der 1/z-Funktion +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{document} +\def\skala{1} +\def\u{3} +\def\punkt#1#2{ + \fill[color=white] #1 circle[radius=0.08]; + \draw[color=#2] #1 circle[radius=0.08]; +} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\fill[color=gray!70,opacity=0.5] (\u,0) circle[radius=\u]; +\fill[color=gray!70,opacity=0.5] (0,\u) circle[radius=\u]; +\fill[color=gray!70,opacity=0.5] (-\u,0) circle[radius=\u]; +\fill[color=gray!70,opacity=0.5] (0,-\u) circle[radius=\u]; + +%\draw[line width=0.5pt] (\u,0) circle[radius=\u]; +%\draw[line width=0.5pt] (0,\u) circle[radius=\u]; +%\draw[line width=0.5pt] (-\u,0) circle[radius=\u]; +%\draw[line width=0.5pt] (0,-\u) circle[radius=\u]; + +\draw[->] ({-0.5-2*\u},0) -- ({2*\u+0.8},0) + coordinate[label={$\operatorname{Re}z$}]; +\draw[->] (0,{-0.5-2*\u}) -- (0,{2*\u+0.8}) + coordinate[label={$\operatorname{Im}z$}]; + +\draw[color=darkgreen,line width=1.4pt] (0,0) circle[radius=\u]; +\node[color=darkgreen] at (70:\u) [above] {$\gamma_+$}; +\node[color=darkgreen] at (-70:\u) [below] {$\gamma_-$}; +\node at (\u,0) [above right] {$1$}; +\node at (0,\u) [above left] {$i$}; +\node at (-\u,0) [above left] {$-1$}; +\node at (0,-\u) [below left] {$-i$}; + +\punkt{(\u,0)}{black} +\punkt{(-\u,0)}{black} +\punkt{(0,\u)}{black} +\punkt{(0,-\u)}{black} + +\punkt{({0.5*\u},{0.5*\u})}{red} +\punkt{({-0.5*\u},{0.5*\u})}{red} +\punkt{({-0.5*\u},{-0.5*\u})}{red} +\punkt{({0.5*\u},{-0.5*\u})}{red} + +\node[color=red] at ({0.5*\u},{0.5*\u}) [above] {$(1+i)\frac{\sqrt{2}}{2}$}; +\node[color=red] at ({0.5*\u},{-0.5*\u}) [below] {$(1-i)\frac{\sqrt{2}}{2}$}; +\node[color=red] at ({-0.5*\u},{-0.5*\u}) [below] {$(-1-i)\frac{\sqrt{2}}{2}$}; +\node[color=red] at ({-0.5*\u},{0.5*\u}) [above] {$(-1+i)\frac{\sqrt{2}}{2}$}; + +\fill[color=white] (0,0) circle[radius=0.2]; + +\end{tikzpicture} +\end{document} + |