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High Quality Content by WIKIPEDIA articles! In mathematics, the radius of convergence of a power series is a quantity, either a non-negative real number or , that represents a domain (within the radius) in which the series will converge. Within the radius of convergence, a power series converges absolutely and uniformly on compacta as well. If the series converges, it is the Taylor series of the analytic function to which it converges inside its radius of convergence.