Row convergence of algebraic approximations

Abstract

An 𝗻 algebraic function of degree 𝑝 satisfies an algebraic equation of degree 𝑝, whose polynomial coefficients have maximum degrees given by the vector n. If a function which is analytic at the origin is approximated by an 𝗻 algebraic function of degree 𝑝, the table of approximations is a table of dimension 𝑝 + 1. Under suitable conditions, the sequence of algebraic approximations along an arbitrary "row" (a line parallel to an arbitrary axis in the table), converges to a given meromorphic function, uniformly on a suitable compact set.