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Generic approximation of entire functions by their Pad\'{e} approximants hasbeen achieved in the past (\cite{3}). In the present article we obtain genericapproximation of holomorphic functions on arbitrary open sets by sequences oftheir Pad\'{e} approximants. Similar results hold with functions smooth on theboundary of their domain of definition. In addition, the approximation is validsimultaneously with respect to all centers of expansion.

Generic approximation of functions by their Pad\'{e} approximants