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 | References | Similar Articles | Additional Information

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.

**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