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author | Patrik Müller <patrik.mueller@ost.ch> | 2022-03-07 17:19:47 +0100 |
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committer | Patrik Müller <patrik.mueller@ost.ch> | 2022-03-07 17:19:47 +0100 |
commit | 403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0 (patch) | |
tree | d62c8fdeeef41457d1235d50edc917c31a70ba91 /buch/papers/laguerre/definition.tex | |
parent | Vorlesungsnotizen für Woche 3 (diff) | |
download | SeminarSpezielleFunktionen-403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0.tar.gz SeminarSpezielleFunktionen-403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0.zip |
Start paper about Laguerre polynomials
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-rw-r--r-- | buch/papers/laguerre/definition.tex | 48 |
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diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex new file mode 100644 index 0000000..5f6d8bd --- /dev/null +++ b/buch/papers/laguerre/definition.tex @@ -0,0 +1,48 @@ +% +% 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} |