q-Hypergeometric Orthogonal Polynomials with q=-1

2024/10/17 by Luis Verde‐Star, Verde-Star, Luis
Mathematics · #33C45 #33D45 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2410.14068

openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain some properties of a class A of q-hypergeometric orthogonal polynomials with q=-1, described by a uniform parametrization of the recurrence coefficients. We construct a class C of complementary -1 polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials and their complementary polynomials and other known -1 polynomials. We introduce some new examples of -1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra.

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