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Diffstat (limited to 'buch/chapters/080-funktionentheorie/images/gammapfad.tex')
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diff --git a/buch/chapters/080-funktionentheorie/images/gammapfad.tex b/buch/chapters/080-funktionentheorie/images/gammapfad.tex new file mode 100644 index 0000000..cf24c95 --- /dev/null +++ b/buch/chapters/080-funktionentheorie/images/gammapfad.tex @@ -0,0 +1,54 @@ +% +% 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} + |