On inversion and connection coefficients for basic hypergeometric polynomials

TL;DR

This paper introduces a general method for explicitly calculating inversion and connection coefficients between basic hypergeometric polynomial sets, with applications to $d$-orthogonal polynomials and the $q$-Askey scheme.

Contribution

It provides a novel, general approach to express inversion and connection coefficients for basic hypergeometric polynomials, expanding the analytical tools available for these functions.

Findings

Derived explicit expansion formulas for $d$-orthogonal basic hypergeometric polynomials.

Connected various polynomial families within the $q$-Askey scheme.

Enhanced understanding of relationships between different basic hypergeometric polynomial sets.

Abstract

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric polynomials and we derive expansion formulae corresponding to all the families within the $q$-Askey scheme.