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Combinatorial orthogonal expansions


Authors: A. de Médicis and D. Stanton
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
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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 [Enhancements On Off] (What's this?)

  • 1 R. Askey, Linearization of the product of orthogonal polynomials, Problems in Analysis (R. Gunning, ed.), Princeton Univ. Press, Princeton, NJ, 1970, pp. (223--228), MR 49:9525.
  • 2 ------, Orthogonal expansions with positive coefficients. II, SIAM J. Math. Anal. 2 (1971), 340--346, MR 45:5650.
  • 3 T. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, New York, 1978, MR 58:1979.
  • 4 R. Szwarc, Orthogonal polynomials and a discrete boundary value problem I, SIAM J. Math. Anal. 23 (1992), 959--964, MR 93i:33007.
  • 5 ------, Orthogonal expansions and a discrete boundary value problem II, SIAM J. Math. Anal. 23 (1992), 965--969, MR 93i:33007.
  • 6 G. Viennot, Une théorie combinatoire des polynômes orthogonaux généraux, Lecture Notes, UQAM, 1983.

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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

DOI: https://doi.org/10.1090/S0002-9939-96-03262-5
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
Article copyright: © Copyright 1996 American Mathematical Society

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