Abstract: The purpose of this paper is to construct a generalized Gaussian quadrature rule based on the divided differences of the integrand at the zeros of the n-th Chebyshev polynomial of the first kind. Another similar quadrature rule based on the divided differences at the zeros of the n-th Chebyshev polynomial of the second kind is also considered. The obtained results include some existing results as special cases. The interesting thing here is that these new results are closely related to the so-called Gauss-Turan quadrature formulas.

Key words: Generalized Gaussian quadrature rule, Gauss-Turan quadrature, s-orthogonal polynomial, Cotes number, Highest algebraic degree of precision