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This article is cited in 2 scientific papers (total in 2 papers)
An Introduction to the $q$-Laguerre–Hahn Orthogonal $q$-Polynomials
Abdallah Ghressi, Lotfi Khériji, Mohamed Ihsen Tounsi Institut Supérieur des Sciences Appliquées et de Technologies de Gabès, Rue Omar Ibn El-Khattab 6072 Gabès, Tunisia
Abstract:
Orthogonal $q$-polynomials associated with $q$-Laguerre–Hahn form will be studied as a generalization of the
$q$-semiclassical forms via a suitable $q$-difference equation. The concept of class and a criterion to determinate it will be given. The $q$-Riccati equation satisfied by the corresponding formal Stieltjes series is obtained. Also, the structure relation is established. Some illustrative examples are highlighted.
Keywords:
orthogonal $q$-polynomials; $q$-Laguerre–Hahn form; $q$-difference operator; $q$-difference equation; $q$-Riccati equation.
Received: February 14, 2011; in final form September 26, 2011; Published online October 4, 2011
Citation:
Abdallah Ghressi, Lotfi Khériji, Mohamed Ihsen Tounsi, “An Introduction to the $q$-Laguerre–Hahn Orthogonal $q$-Polynomials”, SIGMA, 7 (2011), 092, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma650 https://www.mathnet.ru/eng/sigma/v7/p92
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