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Computations of Definite Integrals Using the Residue Theorem

  • Daniel Alpay
Chapter

Abstract

We have seen in Chapter  5 how the fundamental theorem of calculus for line integrals, or Cauchy’s theorem, allow us to compute (in general real) definite integrals such as the Fresnel integrals. In that chapter no residues are computed. The approach in the present chapter is different. The main player is the residue theorem. There are numerous kinds of definite integrals which one can compute using this theorem, and in the present chapter we do not try to be exhaustive.

Keywords

Real Line Dominate Convergence Theorem Residue Theorem Hankel Matrix Positive Imaginary Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Daniel Alpay
    • 1
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of MathematicsChapman UniversityOrangeUSA

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