On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

TL;DR

This paper establishes a limit formula connecting q-Racah and big q-Jacobi polynomials, extending to multi-parameter cases involving various orthogonal polynomials, and provides conceptual insights into other polynomial limits.

Contribution

It introduces a new limit formula from q-Racah to big q-Jacobi polynomials and extends it to multi-parameter cases, offering a unified perspective on polynomial limits.

Findings

Derived a limit formula from q-Racah to big q-Jacobi polynomials.

Extended the limit to multi-parameter cases involving Hahn and Jacobi polynomials.

Provided a conceptual framework for limits from Askey-Wilson to Wilson and Racah polynomials.

Abstract

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey-Wilson to Wilson polynomials and from q-Racah to Racah polynomials are given in a more conceptual way.