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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.
pdf (417 kb)
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