Generic Approximation of functions by their pad\'{e} approximants, I

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.