On the limit of non-standard q-Racah polynomials

TL;DR

This paper investigates the limit transitions of non-standard q-Racah polynomials to other q-orthogonal polynomials, ensuring the preservation of orthogonality and recurrence relations.

Contribution

It provides a detailed analysis of how non-standard q-Racah polynomials transition to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials while maintaining key properties.

Findings

Established limit relations preserving orthogonality.

Derived recurrence relations for the limit polynomials.

Extended the understanding of q-polynomial hierarchies.

Abstract

The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials such that the orthogonality properties and the three-term recurrence relations remain valid.