# Sinc Integrals

Borwein, David

### Abstract

This talk will review some of the work conducted with my son Jonathan (and others) over the past dozen years on properties of integrals involving the function sinc*TeX Embedding failed!* One striking example of such a property is that

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for *TeX Embedding failed!*, but for *TeX Embedding failed!* the integral is strictly less than *TeX Embedding failed!* Integrals such as these can be related to volumes of symmetric convex polyhedra.

The review is based on material in three papers:

1. D. Borwein and J.M Borwein, Some remarkable properties of sinc and related integrals, *TeX Embedding failed!* *TeX Embedding failed!* (2001), 73 - 90.

2. D. Borwein , J.M Borwein, and B. A. Mares Jr., Multi-variable sinc integrals and volumes of polyhedra, *TeX Embedding failed!* *TeX Embedding failed!* (2002), 189 - 208.

3. D. Borwein , J.M Borwein, and I.E. Leonard, *TeX Embedding failed!* norms and the sinc function, *TeX Embedding failed!* *TeX Embedding failed!* (2010), 528 - 539.

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