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

dedicated to Willard Miller on the occasion of his retirement; the unnumbered formula after (2.5) is corrected

References in corpus (1)

• The Askey scheme as a four-manifold with corners

Cited by in corpus (3)

• Dunkl shift operators and Bannai-Ito polynomials
• A "Continuous" Limit of the Complementary Bannai-Ito Polynomials: Chihara Polynomials
• On the limit of non-standard q-Racah polynomials