Orthogonal Laurent polynomials and quadrature formulas for unbounded intervals: II. Interpolatory rules Original Research Article

We study the convergence of quadrature formulas for integrals over the positive real line with an arbitrary (possibly complex) distribution function. The nodes of the quadrature formulas are the zeros of orthogonal Laurent polynomials with respect to an auxiliary distribution function and a certain nesting. The quadratures are called interpolatory (product) formulas. The class of functions for which convergence holds is characterized in terms of the moments of the auxiliary distribution function. We also include the convergence analysis of related two-point Padé-type approximants to the Stieltjes transform of the given distribution function. Finally, some illustrative numerical examples are also given.