Identities for $q$-ultraspherical polynomials and Jacobi functions
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- by H. T. Koelink PDF
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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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Additional 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