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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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1572-9176
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Volume 17, Issue 3

Issues

Orthogonal polynomials with respect to the form u = λ(xa)–1 ν + δb

Mabrouk Sghaier
  • Institut Supérieur d'Informatique de Medenine, Route Djerba – Km 3 – Ibn Khaldoun – 4119 Medenine, Tunisia. E-mail:
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Published Online: 2010-07-30 | DOI: https://doi.org/10.1515/gmj.2010.027

Abstract

We study properties of the form (linear functional) u = λ(xa)–1 ν + δb , where ν is a regular form. We give a necessary and sufficient condition for the regularity of the form u. The coefficients of a three-term recurrence relation, satisfied by the corresponding sequence of orthogonal polynomials, are given explicitly. The semi-classical character of the founded families is studied. We conclude by giving some examples.

Keywords.: Orthogonal polynomials; recurrence relation; semi-classical forms

About the article

Received: 2008-03-24

Revised: 2008-06-02

Published Online: 2010-07-30

Published in Print: 2010-09-01


Citation Information: Georgian Mathematical Journal, Volume 17, Issue 3, Pages 581–596, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2010.027.

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