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Proceedings of the American Mathematical Society

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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