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authortim30b <tim.toenz@ost.ch>2022-05-18 13:53:24 +0200
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-%
-% 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