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| author | Andreas Müller <andreas.mueller@ost.ch> | 2022-03-07 21:09:47 +0100 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2022-03-07 21:09:47 +0100 |
| commit | 5812064b4f37ce9bb8219f5c6ad78ec5ad2356ed (patch) | |
| tree | 2e8be71f49833559e8103b6ce73489c4c45647b9 /buch/papers/laguerre/quadratur.tex | |
| parent | Merge pull request #2 from ntobler/master (diff) | |
| parent | Change title, name, added some formulas and structured paper (diff) | |
| download | SeminarSpezielleFunktionen-5812064b4f37ce9bb8219f5c6ad78ec5ad2356ed.tar.gz SeminarSpezielleFunktionen-5812064b4f37ce9bb8219f5c6ad78ec5ad2356ed.zip | |
Merge pull request #3 from p1mueller/master
Laguerre Polynomials: Added title, author name and paper structure (first draft)
Diffstat (limited to 'buch/papers/laguerre/quadratur.tex')
| -rw-r--r-- | buch/papers/laguerre/quadratur.tex | 29 |
1 files changed, 29 insertions, 0 deletions
diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex new file mode 100644 index 0000000..8ab1af5 --- /dev/null +++ b/buch/papers/laguerre/quadratur.tex @@ -0,0 +1,29 @@ +% +% 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} + |