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Combinatorial orthogonal expansions
Author(s):
A.
de Médicis;
D.
Stanton
Journal:
Proc. Amer. Math. Soc.
124
(1996),
469-473.
MSC (1991):
Primary 42C05, 05E35
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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:
- 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
Address at time of publication:
LACIM, Département de Mathématiques, UQAM, C.P. 8888, succ. A, Montréal, Québec, Canada H3C 3P8
Email:
medicis@lacim.uqam.ca
D.
Stanton
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
stanton@s2.math.umn.edu
DOI:
10.1090/S0002-9939-96-03262-5
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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