A multivariate convergence theorem of the “de Montessus de Ballore” type

AbstractThe univariate theorem of “de Montessus de Ballore” proves the convergence of column sequences of Padé approximants for functions f(z) meromorphic in a disk, in case the number of poles of f(z) and their multiplicity is known in advance. We prove here a multivariate anologon for the case of “simple” poles and for the general order Padé approximants as introduced by Cuyt and Verdonk (1984)