Computations of Definite Integrals Using the Residue Theorem

Daniel Alpay
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Daniel Alpay: Ben-Gurion University of the Negev, Department of Mathematics

Chapter Chapter 8 in A Complex Analysis Problem Book, 2016, pp 381-413 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-42181-0_8

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