ABSTRACT
From the results demonstrated in Section 6.14 of Chapter 6, it follows that, if two functions are analytic in a domain D and they coincide in a neighborhood of any point a in D or only along a path segment terminating a point a in D or only at an infinite number of distinct points with a limit point a ∈ D, then the two functions are identically the same in D. It follows that an analytic function defined in a domain D is completely determined by its values over any of such sets of points. This remarkable feature of analytic functions is extremely helpful in the study of analytic functions from a general viewpoint by virtue of what is known as analytic continuation.
