We study the problem of analytic continuation of a power series across an open arc on the boundary ofthe circle of convergence. The answer is given in terms of a meromorphic function of a special formthat interpolates the coefficients of the series. We find the conditions for the sum of the series to extendanalytically to a neigbourhood of the arc, to a sector defined by the arc, or to the whole complex planeexcept some arc on the convergence disk
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