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On Jacobi and continuous Hahn polynomials


Author: H. T. Koelink
Journal: Proc. Amer. Math. Soc. 124 (1996), 887-898
MSC (1991): Primary 33C45, 42A38
MathSciNet review: 1307541
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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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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

DOI: https://doi.org/10.1090/S0002-9939-96-03190-5
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
Article copyright: © Copyright 1996 American Mathematical Society