identity theorem of power series

If the radii of convergence ( of the power seriesMathworldPlanetmathn=0an(z-z0)n  and  n=0bn(z-z0)n  are positive and the sums of the series are equal in infinitely many points which have z0 as an accumulation pointMathworldPlanetmathPlanetmath, then the both series are identical, i.e.  an=bn  for each  n=0, 1, 2,

Title identity theorem of power series
Canonical name IdentityTheoremOfPowerSeries
Date of creation 2013-03-22 16:47:08
Last modified on 2013-03-22 16:47:08
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 4
Author pahio (2872)
Entry type Theorem
Classification msc 30B10
Classification msc 40A30
Related topic IdentityTheoremOfHolomorphicFunctions
Related topic TheoremsOnComplexFunctionSeries