Analytic Functions

  • Luis BarreiraEmail author
  • Claudia Valls
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


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.

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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