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The Ramanujan Journal

, Volume 6, Issue 2, pp 189–208 | Cite as

Multi-Variable Sinc Integrals and Volumes of Polyhedra

  • David Borwein
  • Jonathan M. Borwein
  • Bernard A. MaresJr.
Article

Abstract

We investigate multi-variable integrals of products of sinc functions and show how they may be interpreted as volumes of symmetric convex polyhedra. We then derive an explicit formula for computing such sinc integrals and so equivalently volumes of polyhedra.

multi-variable sinc integrals Fourier transforms convolution Parseval's theorem volumes of polyhedra 

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References

  1. 1.
    D. Borwein and J.M. Borwein, “Some remarkable properties of sinc and related integrals,” Ramanujan J. 5 (2001), 73–90.Google Scholar
  2. 2.
    J.-B. Lasserre, “An analytical expression and an algorithm for the volume of a convex polyhedron,” Journal of Optimization Theory and Applications 39 (1983), 263–277.Google Scholar
  3. 3.
    K.R. Stromberg, Introduction to Classical Real Analysis, Wadsworth, Belmont, CA, 1981.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • David Borwein
    • 1
  • Jonathan M. Borwein
    • 2
  • Bernard A. MaresJr.
    • 3
  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  3. 3.Department of MathematicsBrown UniversityProvidence

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