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where fix) is an integrable function on the finite or infinite interval (a b), and wix) is a given, fixed function such that its moments ck = /(w; xk) (fc = 0, 1, 2, • • • ) exist and c0 > 0. In this paper we consider quadrature formulas which use multiple nodes chosen in advance and other simple nodes which we choose to increase the degree of exactness of the formulas. To be more precise, let ai, a2, ■ ■ • ,ap be real numbers, which are assumed to be fixed, such that the polynomial

Quadrature formulas with simple Gaussian nodes and multiple fixed nodes