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This article is cited in 16 scientific papers (total in 16 papers)
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.
Received: December 12, 2008; in final form July 7, 2009; Published online July 22, 2009
Citation:
Abdallah Ghressi, Lotfi Khériji, “The Symmetrical $H_q$-Semiclassical Orthogonal Polynomials of Class One”, SIGMA, 5 (2009), 076, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma421 https://www.mathnet.ru/eng/sigma/v5/p76
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Abstract page: | 240 | Full-text PDF : | 51 | References: | 32 |
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