Rational approximants to symmetric formal Laurent series

Rational approximants, in the Padé sense, to a given formal Laurent series,F(z)=_–c_kz^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.