More properties of (β,γ)-Chebyshev functions and points

Abstract

Recently, (β,γ)-Chebyshev 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 (β,γ)-Chebyshev functions in the corresponding orthogonality interval.