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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Identities for $q$-ultraspherical polynomials and Jacobi functions
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by H. T. Koelink
Proc. Amer. Math. Soc. 123 (1995), 2479-2487
DOI: https://doi.org/10.1090/S0002-9939-1995-1273504-8

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
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2479-2487
  • MSC: Primary 33C45; Secondary 33D55
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1273504-8
  • MathSciNet review: 1273504