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

[摘要] 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.

[关键词] orthogonal q-polynomials;q-Laguerre–Hahn form;q-dif ference operator;qdif ference equation;q-Riccati equation