Extension of “A multivariate convergence theorem of the “de Montessus de Ballore” type” to multipoles
نویسنده
چکیده
The univariate theorem deals with the case of simple poles as well as with the case t multiple poles. The former means that we have information on the denominator of th meromorphic function while the latter means that we also have information on the derivative ef that denominator. Up to now w-e o+ ,...; prtivcd a multivariate analogon of the univariate d Montessus dc Baiiore theorem for the case of “simple” poles. Before stating the more gener theorem we repeat the necessary notations. Given a Taylor series expansion
منابع مشابه
A multivariate convergence theorem of the “de Montessus de Ballore” type
The univariate theorem of “de Montessus de Ballore” proves the convergence of column sequences of Pad6 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 analogon for the case of “simple” poles and for the general order Pad& approximants as introduced by Cuyt and Verdonk (1984).
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