Hahn polynomials for hypergeometric distribution

Abstract

Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer parameters. Factorization of the Hahn polynomials is explored and used to explain the relation between the index set of orthogonal polynomials and the lattice set in polyhedral domain. In the multivariate case, these constructions lead to nontrivial families of hypergeometric polynomials vanishing on lattice polyhedra. The generating functions and bispectral properties of the orthogonal polynomials are also discussed.

References in corpus (7)

• Bispectrality of multivariable Racah-Wilson polynomials
• A higher rank Racah algebra and the ${\mathbb{Z}}_2^n$ Laplace-Dunkl operator
• Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
• Discrete orthogonal polynomials and difference equations of several variables
• The generic quantum superintegrable system on the sphere and Racah operators
• Connection coefficients for classical orthogonal polynomials of several variables
• Hahn polynomials on polyhedra and quantum integrability

Cited by in corpus (2)

• Representations of the rank two Racah algebra and orthogonal multivariate polynomials
• Factorized $A_2$-Leonard pair