Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Identities for $ q$-ultraspherical polynomials and Jacobi functions

Author: H. T. Koelink
Journal: Proc. Amer. Math. Soc. 123 (1995), 2479-2487
MSC: Primary 33C45; Secondary 33D55
MathSciNet review: 1273504
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33C45, 33D55

Retrieve articles in all journals with MSC: 33C45, 33D55

Additional Information

Keywords: Continuous q-ultraspherical polynomial, q-Hahn polynomial, Jacobi function, ultraspherical polynomial, continuous symmetric Hahn polynomial
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society