  Recently, $(\beta,\gamma)$-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 $(\beta,\gamma)$-Chebyshev
functions in the corresponding orthogonality interval.
