# identity theorem of power series

If the radii of convergence (http://planetmath.org/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  $n=0,\,1,\,2,\,\ldots$

Title identity theorem of power series IdentityTheoremOfPowerSeries 2013-03-22 16:47:08 2013-03-22 16:47:08 pahio (2872) pahio (2872) 4 pahio (2872) Theorem msc 30B10 msc 40A30 IdentityTheoremOfHolomorphicFunctions TheoremsOnComplexFunctionSeries