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authorAndreas Müller <andreas.mueller@ost.ch>2021-12-04 15:33:07 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2021-12-04 15:33:07 +0100
commit9fe06d6b2449b7163c9a7a98e8323b0f90e799bf (patch)
treed35d63bd06fe049a6799cf338437b42535ae8887 /buch/chapters/050-differential/images
parenttitlepage (diff)
downloadSeminarSpezielleFunktionen-9fe06d6b2449b7163c9a7a98e8323b0f90e799bf.tar.gz
SeminarSpezielleFunktionen-9fe06d6b2449b7163c9a7a98e8323b0f90e799bf.zip
neues zur Bessel-Funktion
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-rw-r--r--buch/chapters/050-differential/images/Makefile10
-rw-r--r--buch/chapters/050-differential/images/besselgrid.pdfbin0 -> 28324 bytes
-rw-r--r--buch/chapters/050-differential/images/besselgrid.tex90
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diff --git a/buch/chapters/050-differential/images/Makefile b/buch/chapters/050-differential/images/Makefile
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+#
+# Makefile
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all: besselgrid.pdf
+
+besselgrid.pdf: besselgrid.tex
+ pdflatex besselgrid.tex
+
diff --git a/buch/chapters/050-differential/images/besselgrid.pdf b/buch/chapters/050-differential/images/besselgrid.pdf
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diff --git a/buch/chapters/050-differential/images/besselgrid.tex b/buch/chapters/050-differential/images/besselgrid.tex
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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}
+
+ \node at (-4.5,1.5) {$\Gamma(n+k+1)=\infty$};
+}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\begin{scope}
+ \hintergrund
+ \nsumme
+ \punkte
+ \nachse{black}
+ \kachse
+\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:$m$}];
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+