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Problemy Analiza — Issues of Analysis, 2019, Volume 8(26), Issue 3, Pages 24–37
DOI: https://doi.org/10.15393/j3.art.2019.6290
(Mi pa269)
 

This article is cited in 2 scientific papers (total in 2 papers)

Connection formulas and representations of Laguerre polynomials in terms of the action of linear differential operators

B. Alouia, L. Khérijib

a Université de Gabès, Institut Supérieur des Systèmes Industriels de Gabès, Rue Salah Eddine Elayoubi 6033 Gabès, Tunisia
b Université de Tunis El Manar, Institut Préparatoire aux Etudes d’Ingénieur El Manar, Campus Universitaire El Manar, B.P. 244, 2092 Tunis, Tunisia
Full-text PDF (437 kB) Citations (2)
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Abstract: In this paper, we introduce the notion of $\mathfrak{O}_{\varepsilon}$-classical orthogonal polynomials, where $\mathfrak{O}_{\varepsilon}:=\mathbb{I}+\varepsilon D$ ($\varepsilon\neq0$). It is shown that the scaled Laguerre polynomial sequence $\{a^{-n}L^{(\alpha)}_n(ax)\}_{n\geq0}$, where $a=-\varepsilon^{-1}$, is actually the only $\mathfrak{O}_{\varepsilon}$-classical sequence. As an illustration, we deal with some representations of Laguerre polynomials $L^{(0)}_n(x)$ in terms of the action of linear differential operators on the Laguerre polynomials $L^{(m)}_n(x)$. The inverse connection problem of expanding Laguerre polynomials $L^{(m)}_n(x)$ in terms of $L^{(0)}_n(x)$ is also considered. Furthermore, some connection formulas between the monomial basis $\{x^n\}_{n\geq0}$ and the shifted Laguerre basis $\{L^{(m)}_n(x+1)\}_{n\geq0}$ are deduced.
Keywords: classical polynomials, Laguerre polynomials, lowering and raising operators, structure relations, higher order differential operators, connection formulas.
Received: 14.05.2019
Revised: 01.10.2019
Accepted: 23.09.2019
Bibliographic databases:
Document Type: Article
UDC: 517.587, 517.521.1
MSC: 33C45, 42C05
Language: English
Citation: B. Aloui, L. Khériji, “Connection formulas and representations of Laguerre polynomials in terms of the action of linear differential operators”, Probl. Anal. Issues Anal., 8(26):3 (2019), 24–37
Citation in format AMSBIB
\Bibitem{AloKhe19}
\by B.~Aloui, L.~Kh\'eriji
\paper Connection formulas and representations of Laguerre polynomials in terms of the action of linear differential operators
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 3
\pages 24--37
\mathnet{http://mi.mathnet.ru/pa269}
\crossref{https://doi.org/10.15393/j3.art.2019.6290}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000497499600003}
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  • https://www.mathnet.ru/eng/pa269
  • https://www.mathnet.ru/eng/pa/v26/i3/p24
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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