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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)

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On Jacobi and continuous Hahn polynomials
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by H. T. Koelink PDF
Proc. Amer. Math. Soc. 124 (1996), 887-898 Request permission

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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Additional Information
  • 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
  • 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 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 887-898
  • MSC (1991): Primary 33C45, 42A38
  • DOI: https://doi.org/10.1090/S0002-9939-96-03190-5
  • MathSciNet review: 1307541