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Computations of Definite Integrals Using the Residue Theorem

In: A Complex Analysis Problem Book

Author

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  • Daniel Alpay

    (Ben-Gurion University of the Negev, Department of Mathematics
    Chapman University, Department of Mathematics)

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.

Suggested Citation

  • Daniel Alpay, 2016. "Computations of Definite Integrals Using the Residue Theorem," Springer Books, in: A Complex Analysis Problem Book, edition 2, chapter 0, pages 381-413, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-42181-0_8
    DOI: 10.1007/978-3-319-42181-0_8
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