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Generic approximation of functions by their Padé approximants
Published 1 Jun 2011 in math.CV | (1106.0169v1)
Abstract: Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their Pad\'{e} approximants. Similar results hold with functions smooth on the boundary of their domain of definition. In addition, the approximation is valid simultaneously with respect to all centers of expansion.
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