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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

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CiteScore 2016: 0.36

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Source Normalized Impact per Paper (SNIP) 2016: 0.717

Mathematical Citation Quotient (MCQ) 2016: 0.28

Online
ISSN
1869-6090
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On orthogonal polynomials associated with rational perturbations of linear functional

Mabrouk Sghaier / Mohamed Zaatra
Published Online: 2013-06-05 | DOI: https://doi.org/10.1515/apam-2012-0012

Abstract.

In this paper, we study properties of the linear functional u satisfying

where v is a regular linear functional. We give a necessary and sufficient condition for the regularity of the linear functional u. The coefficients of the three-term recurrence relation, satisfied by the corresponding sequence of orthogonal polynomials, are given explicitly. A study of the semi-classical character of the founded families is done. We conclude with an illustrative example.

Keywords: Orthogonal polynomials; recurrence relation; semi-classical linear functionals

About the article

Received: 2012-06-07

Accepted: 2013-02-09

Published Online: 2013-06-05

Published in Print: 2013-06-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2012-0012.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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