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Erschienen in:
2019 | OriginalPaper | Buchkapitel
10. Analytic Continuation
verfasst von : Hemant Kumar Pathak
Erschienen in: Complex Analysis and Applications
Verlag: Springer Singapore
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Abstract
From the results in Sect. 4.3 of Chap. 4 (see, for instance, Theorem 4.11) it follows that if two functions are analytic in a domain D and if they coincide in a neighborhood of any point \(a \in D\), or only along a path-segment terminating is a point \(a \in D\), or only at an infinite number of distinct points with a limit point \(a \in D\), 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 function from a general view point by virtue of what is known as “analytic continuation”.