Combinatorial orthogonal expansions
HTML articles powered by AMS MathViewer
- 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.
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