Orthogonality Relations for Multivariate Krawtchouk Polynomials
Hiroshi Mizukawa
TL;DR
This paper provides a simplified proof of the orthogonality conditions for multivariate Krawtchouk polynomials, extending known results from the two-variable case to the general multivariate case.
Contribution
It offers a new, straightforward proof of the orthogonality conditions for multivariate Krawtchouk polynomials, generalizing previous two-variable results.
Findings
Simplified proof of orthogonality conditions for multivariate Krawtchouk polynomials
Extension of two-variable orthogonality conditions to the general multivariate case
Clarification of necessary and sufficient conditions for orthogonality
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 Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages, arXiv:1007.4327]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.
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