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.

References in corpus (1)

• The structure relation for Askey-Wilson polynomials

Cited by in corpus (4)

• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials
• Connection preserving deformations and $q$-semi-classical orthogonal polynomials
• Symmetric abstract hypergeometric polynomials