AN INTRODUCTION TO THE Hq-SEMICLASSICAL ORTHOGONAL POLYNOMIALS

Abstract

Orthogonal polynomials associated with H_q- semiclassical linear form will be studied as a generalization of the H_q-classical linear forms. The concept of class and a criterion for determining it will be given. The q-difference equation that the corresponding formal Stieltjes series satisfies is obtained. Also, the structure relation as well as the second order linear q-difference equation are obtained. Some examples of H_q-semiclassical of class 1 were highlighted.