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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 092, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.092 (Mi sigma650) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2011.092
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
Bibliographic databases:
Document Type: Article
MSC: 42C05; 33C45
Language: English
Citation: Abdallah Ghressi, Lotfi Khériji, Mohamed Ihsen Tounsi, “An Introduction to the $q$-Laguerre–Hahn Orthogonal $q$-Polynomials”, SIGMA, 7 (2011), 092, 20 pp.
Citation in format AMSBIB
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\by Abdallah Ghressi, Lotfi Kh\'eriji, Mohamed Ihsen Tounsi
\paper An Introduction to the $q$-Laguerre--Hahn Orthogonal $q$-Polynomials
\jour SIGMA
\yr 2011
\vol 7
\papernumber 092
\totalpages 20
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\crossref{https://doi.org/10.3842/SIGMA.2011.092}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2861184}
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    		Symmetry, Integrability and Geometry: Methods and Applications
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