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authorLordMcFungus <mceagle117@gmail.com>2022-03-08 15:04:08 +0100
committerGitHub <noreply@github.com>2022-03-08 15:04:08 +0100
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-rw-r--r--buch/papers/laguerre/Makefile9
-rw-r--r--buch/papers/laguerre/Makefile.inc16
-rw-r--r--buch/papers/laguerre/definition.tex48
-rw-r--r--buch/papers/laguerre/eigenschaften.tex8
-rw-r--r--buch/papers/laguerre/main.tex20
-rw-r--r--buch/papers/laguerre/packages.tex10
-rw-r--r--buch/papers/laguerre/quadratur.tex29
-rw-r--r--buch/papers/laguerre/references.bib35
-rw-r--r--buch/papers/laguerre/transformation.tex31
-rw-r--r--buch/papers/laguerre/wasserstoff.tex29
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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+++ b/buch/papers/laguerre/Makefile.inc
@@ -0,0 +1,16 @@
+#
+# 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
new file mode 100644
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--- /dev/null
+++ b/buch/papers/laguerre/definition.tex
@@ -0,0 +1,48 @@
+%
+% 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
new file mode 100644
index 0000000..b7597e5
--- /dev/null
+++ 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
new file mode 100644
index 0000000..1fe0f8b
--- /dev/null
+++ b/buch/papers/laguerre/main.tex
@@ -0,0 +1,20 @@
+%
+% 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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--- /dev/null
+++ b/buch/papers/laguerre/packages.tex
@@ -0,0 +1,10 @@
+%
+% 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
index 0000000..8ab1af5
--- /dev/null
+++ b/buch/papers/laguerre/quadratur.tex
@@ -0,0 +1,29 @@
+%
+% 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
new file mode 100644
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--- /dev/null
+++ b/buch/papers/laguerre/references.bib
@@ -0,0 +1,35 @@
+%
+% 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
new file mode 100644
index 0000000..4de86b6
--- /dev/null
+++ b/buch/papers/laguerre/transformation.tex
@@ -0,0 +1,31 @@
+%
+% 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
new file mode 100644
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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}