Estimation of a Stieltjes function expanded to Taylor series at complex conjugate points

Tokarzewski, Stanislaw;Magnus, Alphonse;Gilewicz, Jacek
(2009) 9th Conference on Orthogonal Polynomials, Special Functions and Applications — Location: Marseille(France) (2.July.2007)

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Authors
  • Tokarzewski, Stanislaw
    Author
  • Magnus, AlphonseUCLouvain
    Author
  • Gilewicz, Jacek
    Author
Abstract
Taylor series expansions of a Stieltjes function f in various complex conjugate points are used to construct the so called unified continued fractions (UCF) terminated on P-th step by a remainder f(P)(U) named tail off, We prove that, if f is a Stieltjes function then its tail f(P)(U) is also a Stieltjes function. The estimations off are obtained in what follows. Numerical calculations of the new complex bounds on f generated by complex conjugate input data are carried out. (C) 2009 Elsevier B.V. All rights reserved.
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Tokarzewski, S., Magnus, A., & Gilewicz, J. (2009). Estimation of a Stieltjes function expanded to Taylor series at complex conjugate points. Journal of Computational and Applied Mathematics, 233(3), 835-841. https://doi.org/10.1016/j.cam.2009.02.085 (Original work published 2009)