Combinatorial orthogonal expansions

Authors:
A. de Médicis and D. Stanton

Journal:
Proc. Amer. Math. Soc. **124** (1996), 469-473

MSC (1991):
Primary 42C05, 05E35

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**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****2**Richard Askey,*Orthogonal expansions with positive coefficients. II*, SIAM J. Math. Anal.**2**(1971), 340–346. MR**0296591****3**T. S. Chihara,*An introduction to orthogonal polynomials*, Gordon and Breach Science Publishers, New York-London-Paris, 1978. Mathematics and its Applications, Vol. 13. MR**0481884****4**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**, 10.1137/0523052**5**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**, 10.1137/0523052**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