Convergence of two-point Padé approximants to series of Stieltjes

摘要

In this paper we study the convergence of two-point Padé approximants to Stieltjes series. A Carleman-type condition given by Gragg (1980) in the context of convergence theory for continued fractions is here established in the framework of orthogonal Laurent polynomials (Jones, Njåstad and Thron (1984), Jones and Thron (1981), Njåstad and Thron (1983, 1986)). A bound for the error is also given.