Proceedings of the American Mathematical Society

Author(s): H. T. Koelink
Journal: Proc. Amer. Math. Soc. 124 (1996), 887-898.
MSC (1991): Primary 33C45, 42A38
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Abstract: Jacobi polynomials are mapped onto the continuous Hahn polynomials by the Fourier transform, and the orthogonality relations for the continuous Hahn polynomials then follow from the orthogonality relations for the Jacobi polynomials and the Parseval formula. In a special case this relation dates back to work by Bateman in 1933 and we follow a part of the historical development for these polynomials. Some applications of this relation are given.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 33C45, 42A38

H. T. Koelink
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium
Address at time of publication: Department of Mathematics, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, the Netherlands
Email: koelink@wis.kuleuven.ac.be, koelink@fwi.uva.nl

DOI: 10.1090/S0002-9939-96-03190-5
PII: S 0002-9939(96)03190-5
Keywords: Jacobi polynomials, continuous Hahn polynomials, Fourier transform
Received by editor(s): September 28, 1994
Additional Notes: Supported by a Fellowship of the Research Council of the Katholieke Universiteit Leuven.
Communicated by: Hal L. Smith
Copyright of article: Copyright 1996, American Mathematical Society

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