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author | Patrik Müller <patrik.mueller@ost.ch> | 2022-06-02 15:23:21 +0200 |
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committer | Patrik Müller <patrik.mueller@ost.ch> | 2022-06-02 15:23:21 +0200 |
commit | 85e7d741f78ca0874b42db5cfbd18f4c28a933b3 (patch) | |
tree | 5cbcb6ad9e598ab76af4ed9e092fc0aa5a05336c /buch/papers/laguerre/presentation/sections/gamma.tex | |
parent | Add relative error plots with shift (diff) | |
download | SeminarSpezielleFunktionen-85e7d741f78ca0874b42db5cfbd18f4c28a933b3.tar.gz SeminarSpezielleFunktionen-85e7d741f78ca0874b42db5cfbd18f4c28a933b3.zip |
Add presentation
Diffstat (limited to 'buch/papers/laguerre/presentation/sections/gamma.tex')
-rw-r--r-- | buch/papers/laguerre/presentation/sections/gamma.tex | 50 |
1 files changed, 50 insertions, 0 deletions
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}
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