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Rational approximants to symmetric formal Laurent series

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Abstract

Rational approximants, in the Padé sense, to a given formal Laurent series,F(z)=Σ ∞−∞ c k z k, have been considered by several authors (see [3] for a survey about the different kinds of approximants which can be defined). In this paper, we shall be concerned with symmetric series, that is, when the complex coefficients {c k } +∞−∞ satisfyc −k=c k,k=0, 1,....

Making use of Brezinski's approach [1], for Padé-type approximation to a formal power series, rational approximants toF(z) with prescribed poles are obtained, and their algebraic properties considered. These results will allow us to give an alternative approach for the Padé-Chebyshev approximants.

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References

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de La Laguna, 38721, La Laguna, Tenerife, Spain

    M. Camacho & P. González-Vera

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  1. M. Camacho
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  2. P. González-Vera
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Camacho, M., González-Vera, P. Rational approximants to symmetric formal Laurent series. Numer Algor 3, 117–124 (1992). https://doi.org/10.1007/BF02141921

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