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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}
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