Continuous -1 Hypergeometric Orthogonal Polynomials

2022/09/22 by Jonathan Pelletier, Pelletier, Jonathan, Luc Vinet +3
Mathematics · #33C47 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2209.10727

openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of -1 orthogonal polynomials viewed as q =-1 limits of the q-orthogonal polynomials is pursued. This paper present the continuous polynomials part of the -1 analog of the q-Askey scheme. A compendium of the properties of all the continuous -1 hypergeometric polynomials and their connections is provided.

Related

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• q-Hypergeometric Orthogonal Polynomials with q=-1
• The q and q^-1-symmetric orthogonal polynomials in the q-Askey scheme, their dual polynomials and functions, orthogonality, generating functions and relations and nonterminating q-Chaundy double product representations
• Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
• Additions to the formula lists in "Hypergeometric orthogonal polynomials and their q-analogues" by Koekoek, Lesky and Swarttouw