The Symmetrical Hq-Semiclassical Orthogonal Polynomials of Class One

Abstract

We investigate the quadratic decomposition and duality to classify symmetrical Hq-semiclassical orthogonal q-polynomials of class one where Hq 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.