Quadrature on the half line and two-point Padé approximants to Stieltjes functions. III: The unbounded case (Q1379024)

The authors study approximants \(\sum A_n f(x_n)\) for the integrals \(\int^b_a f(x)d \mu(x)\). In particular if \(\mu\) is a positive measure they establish the relations between these quadrature formuls and two-point Padé and two-point Padé-type approximants for the Stieltjes function \(\int^t_a {d\mu(x) \over x-z}\). The rate of convergence of interpolatory quadrature formulas are given and the case of \(b=\infty\) is analyzed.