On the convergence of general order multivariate Pade-type approximants

In previous papers the convergence of sequences of ''rectangular'' multivariate Pade-type approximants was studied. In other publications definitions of ''triangular'' multivariate Pade-type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls, The numerical examples section illustrates this difference and compares tile obtained results with the approximation power of general order multivariate Pade approximants. (C) 1996 Academic Press, Inc.