Abdallah Ghressi, Lotfi Khériji, “The Symmetrical <nobr>$H_q$</nobr>-Semiclassical Orthogonal Polynomials of Class One”, SIGMA, 2009, Volume 5,076, 22 pp.

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The Symmetrical $H_q$-Semiclassical Orthogonal Polynomials of Class One

Abdallah Ghressi, Lotfi Khériji

Université de Gabès

Abstract: We investigate the quadratic decomposition and duality to classify symmetrical $H_q$-semiclassical orthogonal $q$-polynomials of class one where $H_q$ is the Hahn's operator. For any canonical situation, the recurrence coefficients, the $q$-analog of the distributional equation of Pearson type, the moments and integral or discrete representations are given.

Keywords: quadratic decomposition of symmetrical orthogonal polynomials; semiclassical form; integral representations; $q$-difference operator; $q$-series representations; the $q$-analog of the distributional equation of Pearson type.

MSC: 33C45; 42C05

Received: December 12, 2008; in final form July 7, 2009; Published online July 22, 2009

Language: English

DOI: 10.3842/SIGMA.2009.076