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diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex new file mode 100644 index 0000000..7dca39b --- /dev/null +++ b/buch/papers/laguerre/presentation/sections/gamma.tex @@ -0,0 +1,51 @@ +\section{Gamma-Funktion} + +\begin{frame}{Gamma-Funktion} +\begin{columns} + +\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} +% \caption{Gamma-Funktion} +\end{figure} +\end{column} + +\begin{column}{0.45\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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