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Approximation of a function given by its Laurent series

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Abstract

Approximants are defined for a function which is holomorphic in an annulus. They are shown to have good qualitative properties whenf is meromorphic with a fixed number of poles in the annulus. Their denominators are linked to the reverse orthogonal polynomials of dimension 2, or orthogonal polynomials of dimension −2, following the choice of the parameters. Their numerators then follow the same recurrence relation as the denominators.

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Authors and Affiliations

  1. UFR de Mathématiques, Université de Lille, F-59655, Villeneuve d'Ascq cedex, France

    Jeannette Van Iseghem

  2. Department of Mathematics, University of Bradford, BD7 1DP, Bradford, West-Yorkshire, England

    Peter R. Graves-Morris

Authors
  1. Jeannette Van Iseghem
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  2. Peter R. Graves-Morris
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Additional information

This work was supported by the Human Capital and Mobility Programme of the European Community, Project ROLLS, Contract CHRX-CT93-0416(DG 12 Coma).

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Van Iseghem, J., Graves-Morris, P.R. Approximation of a function given by its Laurent series. Numer Algor 11, 339–351 (1996). https://doi.org/10.1007/BF02142506

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  • DOI: https://doi.org/10.1007/BF02142506

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