Orthogonality Relations for Multivariate Krawtchouk Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011)
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The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Grünbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.
Keywords:
multivariate orthogonal polynomial; hypergeometric function.
@article{SIGMA_2011_7_a16,
author = {Hiroshi Mizukawa},
title = {Orthogonality {Relations} for {Multivariate} {Krawtchouk} {Polynomials}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2011},
volume = {7},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a16/}
}
Hiroshi Mizukawa. Orthogonality Relations for Multivariate Krawtchouk Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a16/
[1] Griffiths R. C., “Orthogonal polynomials on the multinomial distribution”, Austral. J. Statist., 13 (1971), 27–35 | DOI | MR | Zbl
[2] Grünbaum F. A., Rahman M., “On a family of 2-variable orthogonal Krawtchouk polynomials”, SIGMA, 6 (2010), 090, 12 pp., arXiv: 1007.4327 | DOI | MR
[3] Mizukawa H., “Zonal spherical functions on the complex reflection groups and $(m+1,n+1)$-hypergeometric functions”, Adv. Math., 184 (2004), 1–17 | DOI | MR | Zbl
[4] Mizukawa H., Tanaka H., “$(n+1,m+1)$-hypergeometric functions associated to character algebras”, Proc. Amer. Math. Soc., 132 (2004), 2613–2618 | DOI | MR | Zbl