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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/transformation.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/transformation.tex | 31 |
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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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