10 files changed, 235 insertions, 0 deletions
diff --git a/buch/papers/laguerre/Makefile b/buch/papers/laguerre/Makefile
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+#
+# Makefile -- make file for the paper laguerre
+#
+# (c) 2020 Prof Dr Andreas Mueller
+#
+
+images:
+	@echo "no images to be created in laguerre"
+
diff --git a/buch/papers/laguerre/Makefile.inc b/buch/papers/laguerre/Makefile.inc
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+#
+# Makefile.inc -- dependencies for this article
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+dependencies-laguerre =						\
+	papers/laguerre/packages.tex					\
+	papers/laguerre/main.tex					\
+	papers/laguerre/references.bib				\
+	papers/laguerre/definition.tex					\
+	papers/laguerre/eigenschaften.tex				\
+	papers/laguerre/quadratur.tex					\
+	papers/laguerre/transformation.tex				\
+	papers/laguerre/wasserstoff.tex	
+
+
diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex
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+%
+% definition.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Definition
+\label{laguerre:section:definition}}
+\rhead{Definition}
+
+\begin{align}
+    x y''(x) + (1 - x) y'(x) + n y(x)
+    =
+    0 
+    \label{laguerre:dgl}
+\end{align}
+
+\begin{align}
+    L_n(x)
+    =
+    \sum_{k=0}^{n} 
+    \frac{(-1)^k}{k!}
+    \begin{pmatrix}
+        n \\
+        k
+    \end{pmatrix}
+    x^k
+    \label{laguerre:polynom}
+\end{align}
+
+\begin{align}
+    x y''(x) + (\alpha + 1 - x) y'(x) + n y(x)
+    =
+    0 
+    \label{laguerre:generell_dgl}
+\end{align}
+
+\begin{align}
+    L_n^\alpha (x)
+    =
+    \sum_{k=0}^{n} 
+    \frac{(-1)^k}{k!}
+    \begin{pmatrix}
+        n + \alpha \\
+        n - k
+    \end{pmatrix}
+    x^k
+    \label{laguerre:polynom}
+\end{align}
diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex
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+++ b/buch/papers/laguerre/eigenschaften.tex
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+%
+% eigenschaften.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Eigenschaften
+\label{laguerre:section:eigenschaften}}
+\rhead{Eigenschaften}
+\ No newline at end of file
diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex
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+++ b/buch/papers/laguerre/main.tex
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+%
+% main.tex -- Paper zum Thema Laguerre-Polynome
+%
+% (c) 2020 Hochschule Rapperswil
+%
+\chapter{Laguerre-Polynome\label{chapter:laguerre}}
+\lhead{Laguerre-Polynome}
+\begin{refsection}
+\chapterauthor{Patrik Müller}
+
+Hier kommt eine Einleitung.
+
+\input{papers/laguerre/definition}
+\input{papers/laguerre/eigenschaften}
+\input{papers/laguerre/quadratur}
+\input{papers/laguerre/transformation}
+\input{papers/laguerre/wasserstoff}
+
+\printbibliography[heading=subbibliography]
+\end{refsection}
diff --git a/buch/papers/laguerre/packages.tex b/buch/papers/laguerre/packages.tex
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+++ b/buch/papers/laguerre/packages.tex
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+%
+% packages.tex -- packages required by the paper laguerre
+%
+% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+
+% if your paper needs special packages, add package commands as in the
+% following example
+\usepackage{derivative}
+
diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex
new file mode 100644
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+++ b/buch/papers/laguerre/quadratur.tex
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+%
+% quadratur.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Gauss-Laguerre Quadratur
+\label{laguerre:section:quadratur}}
+
+\begin{align}
+    \int_a^b f(x) w(x)
+    \approx
+    \sum_{i=1}^N f(x_i) A_i
+    \label{laguerre:gaussquadratur}
+\end{align}
+
+\begin{align}
+    \int_{0}^{\infty} f(x) e^{-x} dx 
+    \approx
+    \sum_{i=1}^{N} f(x_i) A_i
+    \label{laguerre:laguerrequadratur}
+\end{align}
+
+\begin{align}
+    A_i 
+    = 
+    \frac{x_i}{(n + 1)^2 \left[ L_{n + 1}(x_i)\right]^2}
+    \label{laguerre:quadratur_gewichte}
+\end{align}
+
diff --git a/buch/papers/laguerre/references.bib b/buch/papers/laguerre/references.bib
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+++ b/buch/papers/laguerre/references.bib
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+%
+% references.bib -- Bibliography file for the paper laguerre
+%
+% (c) 2020 Autor, Hochschule Rapperswil
+%
+
+@online{laguerre:bibtex,
+	title = {BibTeX},
+	url = {https://de.wikipedia.org/wiki/BibTeX},
+	date = {2020-02-06},
+	year = {2020},
+	month = {2},
+	day = {6}
+}
+
+@book{laguerre:numerical-analysis,
+	title = {Numerical Analysis},
+	author = {David Kincaid and Ward Cheney},
+	publisher = {American Mathematical Society},
+	year = {2002},
+	isbn = {978-8-8218-4788-6},
+	inseries = {Pure and applied undegraduate texts},
+	volume = {2}
+}
+
+@article{laguerre:mendezmueller,
+        author = { Tabea Méndez and Andreas Müller },
+        title = { Noncommutative harmonic analysis and image registration },
+        journal = { Appl. Comput. Harmon. Anal.},
+        year = 2019,
+        volume = 47,
+        pages = {607--627},
+        url = {https://doi.org/10.1016/j.acha.2017.11.004}
+}
+
diff --git a/buch/papers/laguerre/transformation.tex b/buch/papers/laguerre/transformation.tex
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+++ b/buch/papers/laguerre/transformation.tex
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+%
+% transformation.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Laguerre Transformation
+\label{laguerre:section:transformation}}
+\begin{align}
+    L \left\{ f(x) \right\}
+    =
+    \tilde{f}_\alpha(n)
+    =
+    \int_0^\infty e^{-x} x^\alpha L_n^\alpha(x) f(x) dx
+    \label{laguerre:transformation}
+\end{align}
+
+\begin{align}
+    L^{-1} \left\{ \tilde{f}_\alpha(n) \right\}
+    =
+    f(x)
+    =
+    \sum_{n=0}^{\infty} 
+    \begin{pmatrix}
+        n + \alpha \\
+        n
+    \end{pmatrix}^{-1}
+    \frac{1}{\Gamma(\alpha + 1)}
+    \tilde{f}_\alpha(n)
+    L_n^\alpha(x)
+    \label{laguerre:inverse_transformation}
+\end{align}
+\ No newline at end of file
diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex
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--- /dev/null
+++ b/buch/papers/laguerre/wasserstoff.tex
@@ -0,0 +1,29 @@
+%
+% wasserstoff.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Radialer Schwingungsanteil eines Wasserstoffatoms
+\label{laguerre:section:radial_h_atom}}
+
+\begin{align}
+    \nonumber
+    - \frac{\hbar^2}{2m} 
+    &
+    \left( 
+        \frac{1}{r^2} \pdv{}{r}
+        \left( r^2 \pdv{}{r} \right)
+        +
+        \frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta}
+        \left( \sin \vartheta \pdv{}{\vartheta} \right)
+        +
+        \frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi}
+    \right)
+    u(r, \vartheta, \varphi)
+    \\
+    & -
+    \frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi)
+    =
+    E u(r, \vartheta, \varphi)
+    \label{laguerre:pdg_h_atom}
+\end{align}