Analytic Continuation

Hemant Kumar Pathak ()
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Hemant Kumar Pathak: Pt. Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 10 in Complex Analysis and Applications, 2019, pp 715-752 from Springer

Abstract: 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”.

Date: 2019
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DOI: 10.1007/978-981-13-9734-9_10

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