From 85e7d741f78ca0874b42db5cfbd18f4c28a933b3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Thu, 2 Jun 2022 15:23:21 +0200
Subject: Add presentation

---
 .../laguerre/presentation/sections/gamma.tex       | 50 ++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 buch/papers/laguerre/presentation/sections/gamma.tex

(limited to 'buch/papers/laguerre/presentation/sections/gamma.tex')

diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex
new file mode 100644
index 0000000..37f4a0b
--- /dev/null
+++ b/buch/papers/laguerre/presentation/sections/gamma.tex
@@ -0,0 +1,50 @@
+\section{Gamma-Funktion}
+
+\begin{frame}{Gamma-Funktion}
+\begin{columns}
+
+\begin{column}{0.48\textwidth}
+\begin{figure}[h]
+\centering
+% \scalebox{0.51}{\input{../images/gammaplot.pdf}}
+\includegraphics[width=1\textwidth]{../images/gammaplot.pdf}
+% \caption{Gamma-Funktion}
+\end{figure}
+\end{column}
+
+\begin{column}{0.52\textwidth}
+Verallgemeinerung der Fakultät
+\begin{align*}
+\Gamma(n) = (n-1)!    
+\end{align*}
+
+Integralformel
+\begin{align*}
+\Gamma(z) 
+=
+\int_0^\infty x^{z-1} e^{-x} \, dx
+,\quad
+\operatorname{Re} z > 0
+\end{align*}
+
+Funktionalgleichung
+\begin{align*}
+z \Gamma(z)
+=
+\Gamma(z + 1)
+\end{align*}
+
+Reflektionsformel
+\begin{align*}
+\Gamma(z) \Gamma(1 - z)
+=
+\frac{\pi}{\sin \pi z}
+, \quad
+\text{für }
+z \notin \mathbb{Z}
+\end{align*}
+
+\end{column}
+\end{columns}
+
+\end{frame}
\ No newline at end of file
-- 
cgit v1.2.1


From 8fb46098cb8e42a94b8e01ecc809f536d5c7efaf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Fri, 3 Jun 2022 07:23:21 +0200
Subject: Minor tweaks of presentation

---
 buch/papers/laguerre/presentation/sections/gamma.tex | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

(limited to 'buch/papers/laguerre/presentation/sections/gamma.tex')

diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex
index 37f4a0b..7dca39b 100644
--- a/buch/papers/laguerre/presentation/sections/gamma.tex
+++ b/buch/papers/laguerre/presentation/sections/gamma.tex
@@ -3,8 +3,9 @@
 \begin{frame}{Gamma-Funktion}
 \begin{columns}
 
-\begin{column}{0.48\textwidth}
+\begin{column}{0.55\textwidth}
 \begin{figure}[h]
+\vspace{-16pt}
 \centering
 % \scalebox{0.51}{\input{../images/gammaplot.pdf}}
 \includegraphics[width=1\textwidth]{../images/gammaplot.pdf}
@@ -12,7 +13,7 @@
 \end{figure}
 \end{column}
 
-\begin{column}{0.52\textwidth}
+\begin{column}{0.45\textwidth}
 Verallgemeinerung der Fakultät
 \begin{align*}
 \Gamma(n) = (n-1)!    
-- 
cgit v1.2.1