Generalized averaged gaussian formulas for certain weight functions

Abstract

In this paper we analyze the generalized averaged Gaussian quadrature formulas and the simplest truncated variant for one of them for some weight functions on the interval [0, 1] considered by Milovanovic in [10]. We shall investigate internality of these formulas for the equivalents of the Jacobi polynomials on this interval and, in some special cases, show the existence of the Gauss-Kronrod quadrature formula. We also include some examples showing the corresponding error estimates for some non-classical orthogonal polynomials.