The Ramanujan Journal

, Volume 5, Issue 1, pp 73–89 | Cite as

Some Remarkable Properties of Sinc and Related Integrals

  • David Borwein
  • Jonathan M. Borwein


Using Fourier transform techniques, we establish inequalities for integrals of the form\(\smallint _0^x \prod\limits_{k = 0}^n {\frac{{\sin (akx)_{} }}{{akx}}dx.} \)

We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.

sinc integrals Fourier transforms convolution Parseval's theorem 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • David Borwein
    • 1
  • Jonathan M. Borwein
    • 2
  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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