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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

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 21, Issue 2


q-Dunkl-classical q-Hermite type polynomials

Youssèf Ben Cheikh / Mohamed Gaied
  • Institut Supérieur d'Informatique et des Techniques de Communication, University of Sousse, 4011, Hammam Sousse, Tunisia
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/ Ali Zaghouani
Published Online: 2014-05-13 | DOI: https://doi.org/10.1515/gmj-2014-0022


In this paper, we introduce two symmetric q-Dunkl-classical orthogonal polynomial sets generalizing the Hermite polynomials as range of discrete q-Hermite polynomials I and II by a suitable orthogonality preserving operator. Then, we state some of their properties: explicit expressions, recurrence relations, generating functions, inversion formulas, linear functionals and components. We conclude by locating these polynomials among orthogonal polynomials generalizing Hermite polynomials and classified according to lowering operators.

Keywords: Orthogonal polynomials; symmetric orthogonal polynomials; q-Dunkl operator; generalized Hermite polynomials; discrete q-Hermite polynomials I and II

MSC: 33C45; 42C05

About the article

Received: 2012-12-24

Accepted: 2013-05-14

Published Online: 2014-05-13

Published in Print: 2014-06-01

Citation Information: Georgian Mathematical Journal, Volume 21, Issue 2, Pages 125–137, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2014-0022.

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