Approximation of a function given by its Laurent series

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