|
SIGMA 7 (2011), 017, 5 pages arXiv:1009.1203
https://doi.org/10.3842/SIGMA.2011.017
Orthogonality Relations for Multivariate Krawtchouk Polynomials
Hiroshi Mizukawa
Department of Mathematics, National Defense Academy of Japan, Yokosuka 239-8686, Japan
Received September 08, 2010, in final form February 18, 2011; Published online February 22, 2011
Abstract
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.
Key words:
multivariate orthogonal polynomial; hypergeometric function.
pdf (290 Kb)
tex (7 Kb)
References
- Griffiths R.C.,
Orthogonal polynomials on the multinomial distribution,
Austral. J. Statist. 13 (1971), 27-35.
- Grünbaum F.A., Rahman M.,
On a family of 2-variable orthogonal Krawtchouk polynomials,
SIGMA 6 (2010), 090, 12 pages,
arXiv:1007.4327.
- Mizukawa H.,
Zonal spherical functions on the complex reflection groups and (m+1,n+1)-hypergeometric functions,
Adv. Math. 184 (2004), 1-17.
- Mizukawa H., Tanaka H.,
(n+1,m+1)-hypergeometric functions associated to character algebras,
Proc. Amer. Math. Soc. 132 (2004), 2613-2618.
|
|