Abstract
In this chapter we introduce the notion of an analytic function as a function that can be represented by power series. In particular, we show that the analytic functions are exactly the holomorphic functions. We also study the notion of a singularity with the help of power series with positive and negative powers—the Laurent series. Finally, we show how to compute integrals of a class of functions with singularities—the meromorphic functions—and we describe applications to the computation of improper integrals in the real line.
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© 2012 Springer-Verlag London
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Barreira, L., Valls, C. (2012). Analytic Functions. In: Complex Analysis and Differential Equations. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-4008-5_4
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DOI: https://doi.org/10.1007/978-1-4471-4008-5_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4007-8
Online ISBN: 978-1-4471-4008-5
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