Hahn, Jacobi, and Krawtchouck polynomials of several variables

2013/09/05 by Yuan Xu, Xu, Yuan
Computer Science · Mathematics · Physics and Astronomy · #33C50 #33C70 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #math.CA #msc:33C50 #msc:33C70

paper · pdf · doi:10.48550/arxiv.1309.1510

22 pages

arxiv created 2013/09/05 · openalex publication_date 2013/09/05 · arxiv updated 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hahn polynomials of several variables can be defined by using the Jacobi polynomials on the simplex as a generating function. Starting from this connection, a number of properties for these two families of orthogonal polynomials are derived. It is shown that the Hahn polynomials appear as connecting coefficients between several families of orthogonal polynomials on the simplex. Closed-form formulas are derived for the reproducing kernels of the Hahn polynomials and Krawtchouck polynomials. As an application, the Poisson kernels for the Hahn polynomials and the Krawtchouck polynomials are shown to be nonnegative.

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