The Laguerre transform of some elementary functions
type: Item
instance of: scholarly article
title: The Laguerre transform of some elementary functions
zbMATH Open document ID: 0539.44003
DOI: 10.4171/ZAA/104
author: O. I. Marichev
author: Hans-Jürgen Glaeske
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1984-01-01T00:00:00Z
review text: The first author [Aequationes Math. 22, 73-85 (1981; Zbl 0462.44002)] has introduced the so called generalized Laguerre transformation \[ {\mathcal I}^{(\alpha)}[f](\nu)=\int^{\infty}_{0}e^{- t}t^{\alpha}L_{\nu}^{(\alpha)}(t)f(t)dt \] where \(L_{\nu}^{(\alpha)}\) are the Laguerre functions of the first kind. In the present paper the following generalized Laguerre transforms are calculated \[ {\mathcal I}^{(\alpha)}[t^{\lambda -1}e^{-pt^ r}\left\{ \begin{matrix} \sin bt^ r\\ \cos bt^ r\end{matrix} \right\}](\nu) \] under suitable conditions on the constants. The result is used to find a particular solution of the following differential equation: \(e^ tD(e^{-t}tD)y(t)=e^{-2t} (t>0)\).
Mathematics Subject Classification ID: 44A20
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 3857711
zbMATH Keywords: generalized Laguerre transformation
zbMATH Keywords: Laguerre functions
reviewed by: Istvan Fenyö
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/104
OpenAlex ID: W2564088415
description: scientific article; zbMATH DE number 3857711