Abdallah Ghressi, Lotfi Khériji, Mohamed Ihsen Tounsi, “An Introduction to the <nobr>$q$</nobr>-Laguerre–Hahn Orthogonal <nobr>$q$</nobr>-Polynomials”, SIGMA, 2011, Volume 7,092, 20 pp.

This article is cited in 3 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.

MSC: 42C05; 33C45

Received: February 14, 2011; in final form September 26, 2011; Published online October 4, 2011

Language: English

DOI: 10.3842/SIGMA.2011.092