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%
% besselgrid.tex -- Indexmenge für die Herleitung der erzeugenden 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{1}
\def\r{0.2}
\def\hintergrund{
\fill[color=gray!40,opacity=0.5]
(-6.3,5.8)
-- (-0.1,-0.4)
-- (6.5,-0.4) -- (6.5,-0.8) -- (-6.3,-0.8) -- cycle;
}
\def\nachse#1{
\draw[->,color=#1] (-6.3,0) -- (6.6,0) coordinate[label={$n$}];
}
\def\kachse{
\draw[->] (0,-0.3) -- (0,6.6) coordinate[label={right:$k$}];
}
\def\machse{
\draw[->] (-0.3,-0.3) -- (6.3,6.3) coordinate[label={above right:$m$}];
}
\def\achsen{
\draw[->] (0,-0.3) -- (0,6.6) coordinate[label={right:$k$}];
\draw[->] (-6.3,0) -- (6.6,0) coordinate[label={$n$}];
\draw[->] (0.3,-0.3) -- (-6.3,6.3) coordinate[label={above right:$m$}];
}
\def\nsumme{
\foreach \n in {-6,...,6}{
\fill[color=red!40,opacity=0.5] ({\n-\r},6.3)
-- ({\n-\r},0) arc (-180:0:\r)
-- ({\n+\r},6.3)
-- cycle;
}
}
\def\msumme{
\foreach \k in {0,...,6}{
\fill[color=blue!20] (6.3,{\k+\r})
-- ({-\k},{\k+\r}) arc (90:270:\r)
-- (6.3,{\k-\r})
-- cycle;
}
}
\def\punkte{
\begin{scope}
\clip (-6.2,-0.2) rectangle (6.2,6.2);
\foreach \x in {1,...,6}{
\foreach \y in {0,...,5}{
\fill[color=gray] ({-\x-\y},\y) circle[radius=0.1];
}
}
\foreach \x in {0,...,12}{
\foreach \y in {0,...,6}{
\fill[color=red] ({\x-\y},\y) circle[radius=0.1];
}
}
\end{scope}
}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\begin{scope}
\hintergrund
\nsumme
\punkte
\nachse{black}
\kachse
\node at (-4.5,1.5) {$\Gamma(n+k+1)=\infty$};
\end{scope}
\begin{scope}[yshift=-7.8cm]
\hintergrund
\msumme
\punkte
\draw[->] (0.3,-0.3) -- (-6.4,6.4) coordinate[label={above right:$k$}];
\draw[->] (-3.3,3) -- (6.6,3) coordinate[label={right:$m$}];
\node at (-4.5,1.5) {$\Gamma(m+1)=\infty$};
\end{scope}
\end{tikzpicture}
\end{document}
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