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.

Keywords

• quadratic decomposition of symmetrical orthogonal polynomials
• semiclassical form
• integral representations
• q-difference operator
• q-series representations
• the q-analog of the distributional equation of Pearson type