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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/transformation.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 '')
| -rw-r--r-- | buch/papers/laguerre/transformation.tex | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/buch/papers/laguerre/transformation.tex b/buch/papers/laguerre/transformation.tex new file mode 100644 index 0000000..4de86b6 --- /dev/null +++ b/buch/papers/laguerre/transformation.tex @@ -0,0 +1,31 @@ +% +% 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}
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