We establish the existence of power series in $\mathbb{C}^N$ with the property that the subsequences of the sequence of partial sums uniformly approach any holomorphic function on any well chosen compact subset outside the set of convergence of the series. We also show that, in a certain sense, most series enjoy this property.

MSC Classifications:

32A05, 32E30 show english descriptions Power series, series of functions
Holomorphic and polynomial approximation, Runge pairs, interpolation 32A05 - Power series, series of functions
32E30 - Holomorphic and polynomial approximation, Runge pairs, interpolation

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