Row Convergence of Algebraic Approximations Original Research Article

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, unitformly on a suitable compact set.