identity theorem of power seriesIdentityTheoremOfPowerSeries2007-03-04 14:39:442007-03-04 14:39:44Theorempower series% this is the default PlanetMath preamble. as your knowledge
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If the \PMlinkname{radii of convergence}{RadiusOfConvergence} of the power series\, $\sum_{n=0}^\infty a_n(z-z_0)^n$\, and\, $\sum_{n=0}^\infty b_n(z-z_0)^n$\, are positive and the sums of the series are equal in infinitely many points which have $z_0$ as an accumulation point, then the both series are identical, i.e.\, $a_n = b_n$\, for each\, $n = 0,\,1,\,2,\,\ldots$