From 403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Mon, 7 Mar 2022 17:19:47 +0100
Subject: Start paper about Laguerre polynomials

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 buch/papers/laguerre/quadratur.tex | 29 +++++++++++++++++++++++++++++
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+%
+% quadratur.tex 
+%
+% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
+%
+\section{Gauss-Laguerre Quadratur
+\label{laguerre:section:quadratur}}
+
+\begin{align}
+    \int_a^b f(x) w(x)
+    \approx
+    \sum_{i=1}^N f(x_i) A_i
+    \label{laguerre:gaussquadratur}
+\end{align}
+
+\begin{align}
+    \int_{0}^{\infty} f(x) e^{-x} dx 
+    \approx
+    \sum_{i=1}^{N} f(x_i) A_i
+    \label{laguerre:laguerrequadratur}
+\end{align}
+
+\begin{align}
+    A_i 
+    = 
+    \frac{x_i}{(n + 1)^2 \left[ L_{n + 1}(x_i)\right]^2}
+    \label{laguerre:quadratur_gewichte}
+\end{align}
+
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