N-point Pade approximants and two-sided estimates of errors on the real axis for Stieltjes functions

摘要

Upper and lower estimates of Stieltjes function by N-point Pade approximants can be obtained using the new general inequality reported by Tokarzewski et al. (Arch. Mech. 54 (2002) 141-153) and rigorously proved in the present paper. In addition, we prove that the multipoint Pade approximants to Stieltjes function are symmetric with respect to the order of choice of the considered points. (c) 2004 Elsevier B.V. All rights reserved.