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author | Andreas Müller <andreas.mueller@ost.ch> | 2022-03-07 21:09:47 +0100 |
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committer | GitHub <noreply@github.com> | 2022-03-07 21:09:47 +0100 |
commit | 5812064b4f37ce9bb8219f5c6ad78ec5ad2356ed (patch) | |
tree | 2e8be71f49833559e8103b6ce73489c4c45647b9 /buch/papers/laguerre/definition.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/definition.tex')
-rw-r--r-- | buch/papers/laguerre/definition.tex | 48 |
1 files changed, 48 insertions, 0 deletions
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} |