S-orthogonality and construction of Gauss-Turلn-type quadrature formulae

Using the theory of s-orthogonality and reinterpreting it in terms of the standard orthogonal polynomials on the real line, we develop a method for constructing Gauss-Turلn-type quadrature formulae. The determination of nodes and weights is very stable. For finding all weights, our method uses an upper triangular system of linear equations for the weights associated with each node. Numerical examples are included.