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Generalizations of the theorem of de Montessus to two-variable approximants

A new proof of the theorem of de Montessus is given which does not depend upon the assumption of normality of the power series from which the Padé approximants are formed. The study is extended to sequences of approximants to double series, generalizations of Padé approximants. Several generalizations of the theorem of de Montessus to these sequences are stated and proved.