# Some Remarkable Properties of Sinc and Related Integrals

Borwein, Jonathan M. and Borwein, David (2001) Some Remarkable Properties of Sinc and Related Integrals. The Ramanujan Journal, 5 (1). pp. 73-90.

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## Abstract

Using Fourier transform techniques, we establish inequalities for integrals of the form $$\int_0^\infty\prod_{k=0}^n \frac{\sin(a_kx)}{a_kx}\,dx.$$ We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.

Item Type: Article pubdom FALSE sinc integrals, Fourier transforms, convolution, Parseval's theorem 42-xx Fourier analysis > 42Axx Fourier analysis in one variable UNSPECIFIED Users 1 not found. 28 Nov 2003 13 Jan 2015 12:17 https://docserver.carma.newcastle.edu.au/id/eprint/249

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