Numerical integration rules near gaussian quadrature

We call a numerical integration formula based on k nodes which is exact for polynomials of degree at most n an (n, k) formula. Gaussian quadrature is the unique (2 k-1, k) formula. In this paper we give a complete description of all (2 k-3, k) formulas, including a characterization of those having all positive weights. © 1973 Hebrew University.