The q-Laguerre matrix polynomials

The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomia...

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Detalles Bibliográficos
Autor principal: Salem, Ahmed
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4851681/
https://www.ncbi.nlm.nih.gov/pubmed/27190749
http://dx.doi.org/10.1186/s40064-016-2178-5
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author Salem, Ahmed
author_facet Salem, Ahmed
author_sort Salem, Ahmed
collection PubMed
description The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given.
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spelling pubmed-48516812016-05-17 The q-Laguerre matrix polynomials Salem, Ahmed Springerplus Research The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given. Springer International Publishing 2016-04-30 /pmc/articles/PMC4851681/ /pubmed/27190749 http://dx.doi.org/10.1186/s40064-016-2178-5 Text en © Salem. 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Salem, Ahmed
The q-Laguerre matrix polynomials
title The q-Laguerre matrix polynomials
title_full The q-Laguerre matrix polynomials
title_fullStr The q-Laguerre matrix polynomials
title_full_unstemmed The q-Laguerre matrix polynomials
title_short The q-Laguerre matrix polynomials
title_sort q-laguerre matrix polynomials
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4851681/
https://www.ncbi.nlm.nih.gov/pubmed/27190749
http://dx.doi.org/10.1186/s40064-016-2178-5
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