Indeterminate moment problem associated with continuous dual q-Hahn polynomials

TL;DR

This paper investigates the indeterminate moment problem linked to continuous dual q-Hahn polynomials in the limit as one parameter approaches infinity, establishing solutions and orthogonality relations for the case q > 1.

Contribution

It introduces a new analysis of the indeterminate moment problem for continuous dual q-Hahn polynomials in a specific limiting case, expanding understanding of their orthogonality properties.

Findings

Solutions to the indeterminate moment problem are identified.

Orthogonality relations for the polynomials are established.

The study focuses on the case q > 1 in the limit.

Abstract

We study a limiting case of the Askey-Wilson polynomials when one of the parameters goes to infinity, namely continuous dual q-Hahn polynomials when q > 1. Solutions to the associated indeterminate moment problem by general theory are found and an orthogonality relation is established.