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.

翻译：最近，$(\beta,\gamma)$-Chebyshev函数及其对应零点作为第一类经典Chebyshev多项式及相关根的一种推广被引入。这类函数构成$[-1,1]$子集上一族正交函数，且确满足三项递推公式。本文进一步呈现了该函数的其他性质，并证明这些性质与经典正交多项式相关的多种结果相吻合。此外，我们证明了关于相应正交区间内$(\beta,\gamma)$-Chebyshev函数根所关联的Lebesgue常数行为的一个猜想。