Dolomites Research Notes on Approximation

This paper is the continuation of a previous work where the authors have introduced a new class of quadrature rules for evaluating the finite Hilbert transform. Such rules are product type formulae based on the filtered de la Vallée Poussin (shortly VP) type approximation. Here, we focus on some particular cases of interest in applications and show that further results can be obtained in such special cases. In particular, we consider an optimal choice of the quadrature nodes for which explicit formulae of the quadrature weights are given and sharper error estimates are stated.