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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Combinatorial orthogonal expansions
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by A. de Médicis and D. Stanton PDF
Proc. Amer. Math. Soc. 124 (1996), 469-473 Request permission

Abstract:

The linearization coefficients for a set of orthogonal polynomials are given explicitly as a weighted sum of combinatorial objects. Positivity theorems of Askey and Szwarc are corollaries of these expansions.
References
  • Richard Askey, Linearization of the product of orthogonal polynomials, Problems in analysis (papers dedicated to Salomon Bochner, 1969) Princeton Univ. Press, Princeton, N. J., 1970, pp. 131–138. MR 0344786
  • Richard Askey, Orthogonal expansions with positive coefficients. II, SIAM J. Math. Anal. 2 (1971), 340–346. MR 296591, DOI 10.1137/0502031
  • T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
  • Ryszard Szwarc, Orthogonal polynomials and a discrete boundary value problem. I, II, SIAM J. Math. Anal. 23 (1992), no. 4, 959–964, 965–969. MR 1166568, DOI 10.1137/0523052
  • Ryszard Szwarc, Orthogonal polynomials and a discrete boundary value problem. I, II, SIAM J. Math. Anal. 23 (1992), no. 4, 959–964, 965–969. MR 1166568, DOI 10.1137/0523052
  • G. Viennot, Une théorie combinatoire des polynômes orthogonaux généraux.
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Additional Information
  • A. de Médicis
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: medicis@lacim.uqam.ca
  • D. Stanton
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: stanton@s2.math.umn.edu
  • Received by editor(s): August 19, 1994
  • Additional Notes: The first author’s work was supported by NSERC funds.
    The second author’s work was supported by NSF grant DMS-9001195.
  • Communicated by: Jeffry N. Kahn
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 469-473
  • MSC (1991): Primary 42C05, 05E35
  • DOI: https://doi.org/10.1090/S0002-9939-96-03262-5
  • MathSciNet review: 1317035