From 5bd294f334dc1d99e3db29996482f0f2cd1c8b49 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Wed, 27 Oct 2021 08:51:17 +0200
Subject: add gamma function section

---
 buch/chapters/040-rekursion/images/gammaplot.tex | 89 ++++++++++++++++++++++++
 1 file changed, 89 insertions(+)
 create mode 100644 buch/chapters/040-rekursion/images/gammaplot.tex

(limited to 'buch/chapters/040-rekursion/images/gammaplot.tex')

diff --git a/buch/chapters/040-rekursion/images/gammaplot.tex b/buch/chapters/040-rekursion/images/gammaplot.tex
new file mode 100644
index 0000000..4e11d32
--- /dev/null
+++ b/buch/chapters/040-rekursion/images/gammaplot.tex
@@ -0,0 +1,89 @@
+%
+% gammaplot.tex -- template for standalon tikz images
+%
+% (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}
+\input{gammapaths.tex}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\definecolor{darkgreen}{rgb}{0,0.8,0}
+
+\draw[->] (-6.1,0) -- (5.3,0) coordinate[label={$z$}];
+\draw[->] (0,-5.1) -- (0,6.4) coordinate[label={right:$\Gamma(z)$}];
+
+\foreach \x in {-1,-2,-3,-4,-5,-6}{
+	\draw (\x,-0.1) -- (\x,0.1);
+	\draw[line width=0.1pt] (\x,-5) -- (\x,6.2);
+}
+\foreach \x in {1,2,3,4,5}{
+	\draw (\x,-0.1) -- (\x,0.1);
+	\node at (\x,0) [below] {$\x$};
+}
+\foreach \y in {-5,-4,-3,-2,-1,1,2,3,4,5,6}{
+	\draw (-0.1,\y) -- (0.1,\y);
+}
+\foreach \y in {1,2,3,4,5,6}{
+	\node at (0,\y) [left] {$\y$};
+}
+\foreach \y in {-1,-2,-3,-4,-5}{
+	\node at (0,\y) [right] {$\y$};
+}
+\foreach \x in {-1,-3,-5}{
+	\node at (\x,0) [below left] {$\x$};
+}
+\foreach \x in {-2,-4,-6}{
+	\node at (\x,0) [above left] {$\x$};
+}
+
+\def\dx{1}
+\def\dy{1}
+
+\begin{scope}
+\clip (-6.1,-5) rectangle (4.3,6.2);
+
+\draw[color=darkgreen,line width=1.4pt] \gammasinplus;
+\draw[color=darkgreen,line width=1.4pt] \gammasinone;
+\draw[color=darkgreen,line width=1.4pt] \gammasintwo;
+\draw[color=darkgreen,line width=1.4pt] \gammasinthree;
+\draw[color=darkgreen,line width=1.4pt] \gammasinfour;
+\draw[color=darkgreen,line width=1.4pt] \gammasinfive;
+\draw[color=darkgreen,line width=1.4pt] \gammasinsix;
+
+\draw[color=red,line width=1.4pt] \gammaplus;
+\draw[color=red,line width=1.4pt] \gammaone;
+\draw[color=red,line width=1.4pt] \gammatwo;
+\draw[color=red,line width=1.4pt] \gammathree;
+\draw[color=red,line width=1.4pt] \gammafour;
+\draw[color=red,line width=1.4pt] \gammafive;
+\draw[color=red,line width=1.4pt] \gammasix;
+
+\end{scope}
+
+\fill[color=blue] (1,1) circle[radius=0.08];
+\node[color=blue] at (1,1-0.2) [below] {$\Gamma(1)=0!$};
+\fill[color=blue] (2,1) circle[radius=0.08];
+\node[color=blue] at (2,1) [below right] {$\Gamma(2)=1!$};
+\fill[color=blue] (3,2) circle[radius=0.08];
+\node[color=blue] at (3,2) [right] {$\Gamma(3)=2!$};
+\fill[color=blue] (4,6) circle[radius=0.08];
+\node[color=blue] at (4,6) [right] {$\Gamma(4)=3!$};
+
+\begin{scope}[xshift=3cm,yshift=-2.4cm]
+	\draw[color=red,line width=1.4pt] (-1,0) -- (0,0);
+	\draw[color=darkgreen,line width=1.4pt] (-1,-0.7) -- (0,-0.7);
+	\node at (0.1,0) [right] {$\Gamma(z)$};
+	\node at (0.1,-0.7) [right] {$\Gamma(z)+\sin\pi z$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
-- 
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