Quadrature on the half-line and two-point Padé approximants to Stieltjes functions—II: Convergence

Let α be a distribution function on [a,b] (0 ⩽ a < b ⩽ +∞) such that the moment ck = ʃbadα(x) exist for all the integers k. The main course of the paper is to give convergence results both for sequences of two-point Padé approximants to the Cauchy transform of the distribution α (Stieltjes function) and for quadrature formulas based on exactly integrating Laurent polynomials. se when dα(x) = k(x)dx, k(x) being a possibly complex function is also considered and estimates of the rate of convergence are given.