circle of convergence

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A circle in the complex plane with the property that converges for all z within a distance R>0 of z0 and diverges for all z for which |zz0|>R. R is the radius of convergence and if the power series converges for the whole of the complex plane then R is infinite. The case where R=0 is trivial since convergence only occurs when |zz0|=0. For points on the circumference of the circle the series may either converge or diverge.

Subjects: Mathematics.

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