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%
% gammapfad.tex -- Pfad zum Beweis der Reflektionsformel der Gamma-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}
\begin{document}
\def\skala{2}
\definecolor{darkred}{rgb}{0.8,0,0}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\draw[->] (-2.55,0) -- (2.7,0) coordinate[label={$\operatorname{Re}z$}];
\draw[->] (0,-2.55) -- (0,2.7,0) coordinate[label={right:$\operatorname{Im}z$}];
\def\repsilon{0.3}
\def\R{2.5}
\def\d{0.04}
\pgfmathparse{asin(\d/sqrt(\R*\R-\d*\d))}
\xdef\A{\pgfmathresult}
\pgfmathparse{asin(\d/sqrt(\repsilon*\repsilon-\d*\d))}
\xdef\a{\pgfmathresult}
\draw[->] (0,0) -- (70:\R);
\node at (70:{0.7*\R}) [right] {$R$};
\draw[->] (0,0) -- (-40:\repsilon);
\node at (-40:\repsilon) [below right] {$\varepsilon$};
\draw[color=darkred,line width=1.4pt]
({\A-180}:\R) arc ({\A-180}:{180-\A}:\R)
--
({-sqrt(\R*\R-\d*\d)},\d)
--
%({-sqrt(\repsilon*\repsilon-\d*\d)},\d)
({180-\a}:\repsilon) arc ({180-\a}:{\a-180}:\repsilon)
--
({-sqrt(\R*\R-\d*\d)},-\d)
--
cycle;
\fill[color=blue] (1,0) circle[radius=0.04];
\node[color=blue] at (1,0) [above] {$1$};
\node[color=darkred] at (120:\R) [above left] {$\gamma$};
\end{tikzpicture}
\end{document}
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