The Symmetrical $H_q$-Semiclassical Orthogonal Polynomials of Class One

Abstract

We investigate the quadratic decomposition and duality to classify symmetrical $H_q$-semiclassical orthogonal $q$-polynomials of class one where $H_q$ is the Hahn's operator. For any canonical situation, the recurrence coefficients, the $q$-analog of the distributional equation of Pearson type, the moments and integral or discrete representations are given.