If is a Power series which is regular for except for Poles within this Circle and except for , at which points the function is assumed continuous when only points are considered, then at least a subsequence of the Padé Approximants are uniformly bounded in the domain formed by removing the interiors of small circles with centers at these Poles and uniformly continuous at for .

Baker, G. A. Jr. The Padé Conjecture and Some Consequences.'' §II.D in Advances in Theoretical Physics, Vol. 1 (Ed. K. A. Brueckner). New York: Academic Press, pp. 23-27, 1965.