analytic continuation by power series

Given a holomorphic function defined on some open set, one techniquefor analytically continuing it to a larger set is by means of powerseries. One picks a point of the region and constructs the Taylorseries of the function about that point. If it turns out that theradius of convergence of the Taylor series is large enough that itcontains points which are not in the original domain, one canextend the function to a larger domain obtrained by adding these points.