More properties of ( ss,gamma)-Chebyshev functions and points

Recently, ( beta, -gamma)-ebyshev functions, as well as the corresponding zeros, have been introduced as a generalization of classical Chebyshev polynomials of the first kind and related roots. They consist of a family of orthogonal functions on a subset of [-1, 1], which indeed satisfies a three-term recurrence formula. In this paper we present further properties, which are proven to comply with various results about classical orthogonal polynomials. In addition, we prove a conjecture concerning the Lebesgue constant's behavior related to the roots of ( beta,gamma)-Chebyshev functions in the corresponding orthogonality interval. (c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

Recently, (beta, -gamma)-ebyshev functions and their zeros have been introduced as a generalization of classical Chebyshev polynomials and related roots. They are a family of orthogonal functions on a subset of [-1, 1] and satisfy a three-term recurrence formula. This paper presents further properties that comply with various results about classical orthogonal polynomials, and proves a conjecture about the behavior of the Lebesgue constant related to the roots of (beta, gamma)-Chebyshev functions.