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

Authors:
Jacek Gilewicz;Maciej Pindor;J. Joachim Telega;Stanisław Tokarzewski
Affiliations:
Centre de Physique Théorique, CNRS, Luminy Case 907, F-13288 Marseille Cedex 09, France;Institute of Theoretical Physics, Warsaw, Hoza 69, 00-681 Warsaw, Poland;Institute of Fundamental Technological Research, &Sacutewiȩȩtokrzyska 21, 00-049 Warsaw, Poland;Institute of Fundamental Technological Research, &Sacutewiȩȩtokrzyska 21, 00-049 Warsaw, Poland
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Year:
2005

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Abstract

Upper and lower estimates of Stieltjes function by N-point Padé 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 Padé approximants to Stieltjes function are symmetric with respect to the order of choice of the considered points.