example of analytic continuation

The functionMathworldPlanetmath defined by


is, as a sum of power series, analytic in the disc of convergence  D={z|z|<1}.  The function


similarly is analytic in the bigger disc  E={z|z-i|<2}.  But we have


thus f(z) and g(z) coincide in the intersection domain DE.  So we can say that g(z) is the analytic continuation of f(z) to the domain  ED.  It is clear that 11-z is the analytic continuation of f(z) to the domain {1}.

Title example of analytic continuation
Canonical name ExampleOfAnalyticContinuation
Date of creation 2013-03-22 16:52:06
Last modified on 2013-03-22 16:52:06
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Example
Classification msc 30B40
Classification msc 30A99
Related topic RadiusOfConvergence
Related topic GeometricSeries
Related topic SetDifference