Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 092, 20 pages      arXiv:1110.0580      https://doi.org/10.3842/SIGMA.2011.092
Contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)”

An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials

Abdallah Ghressi, Lotfi Khériji and Mohamed Ihsen Tounsi
Institut Supérieur des Sciences Appliquées et de Technologies de Gabès, Rue Omar Ibn El-Khattab 6072 Gabès, Tunisia

Received February 14, 2011, in final form September 26, 2011; Published online October 04, 2011

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.

Key words: orthogonal q-polynomials; q-Laguerre-Hahn form; q-difference operator; q-difference equation; q-Riccati equation.

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