Discrete orthogonality of the polynomial sequences in the $q$-Askey scheme

TL;DR

This paper derives weight functions for q-polynomial sequences in the q-Askey scheme, establishing their discrete orthogonality with respect to a quasi-definite moment functional, except for continuous q-Hermite polynomials.

Contribution

It introduces new weight functions that demonstrate discrete orthogonality for a broad class of q-polynomials within the q-Askey scheme, excluding only the continuous q-Hermite case.

Findings

Weight functions for q-linear and q-quadratic lattices derived

Discrete orthogonality established for most q-polynomials in the scheme

Continuous q-Hermite polynomials are an exception

Abstract

We obtain weight functions associated with $q$-linear and $q$-quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional for the Askey-Wilson polynomials and all the polynomial sequences in the q-Askey scheme, with the exception of the continuous $q$-Hermite polynomials.