CECM Colloquium

Wednesday January 24, 2001 From 3:30 - 4:30 in K9509, SFU

Jonathan Michael Borwein, Simon Fraser University

Talks on

Multi-variable Sinc Integrals and the Volumes of Polyhedra

Abstract: Using classical 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.

The first part of this work is available at www.cecm.sfu.ca/preprints in:

David Borwein and Jonathan M. Borwein, ``Some remarkable properties of sinc and related integrals,'' The Ramanujan Journal, in press. [CECM Preprint 99:142]. while later work is joint with B.J. Mares as well.