Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme
Classical Analysis and ODEs
2024-06-21 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, -Racah, big -Jacobi etc.) and they are related to the factorization of the differential or difference operators. Based on other factorizations, we obtain another type of forward and backward shift relations. Essentially, these shift relations shift only the parameters.
Keywords
Cite
@article{arxiv.2301.00678,
title = {Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme},
author = {Satoru Odake},
journal= {arXiv preprint arXiv:2301.00678},
year = {2024}
}
Comments
31 pages. The Rodrigues-type formulas, some comments and reference are added. To appear in J. Math. Anal. Appl