Identities for 𝑞-ultraspherical polynomials and Jacobi functions

Author:

Koelink H. T.

Abstract

A q-analogue of a result by Badertscher and Koornwinder [Canad. J. Math. 44 (1992), 750-773] relating the action of a Hahn polynomial of differential operator argument on ultraspherical polynomials to an ultraspherical polynomial of shifted order and degree is derived. The q-analogue involves q-Hahn polynomials, continuous q-ultraspherical polynomials, and a shift operator. Another limit as q tends to 1 yields an identity for Jacobi functions. Combination with another result of Badertscher and Koornwinder gives a curious formula for Jacobi functions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference18 articles.

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