identity theorem of power series
If the radii of convergence (http://planetmath.org/RadiusOfConvergence) of the power series ∑∞n=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 point
, then the both series are identical, i.e. an=bn for each n=0, 1, 2,…
Title | identity theorem of power series |
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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 |