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

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