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It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turr an, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable. 0. Introduction The idea of constructing quadrature rules that are exact for rational functions with prescribed poles,… (More)

The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal poly-nomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision… (More)

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