Some remarks on sinc integrals and their connection with combinatorics, geometry and probability

TL;DR

This paper offers a new combinatorial and geometrical approach to evaluating certain sinc integrals, linking them to combinatorics, geometry, and probability, and providing insights into related identities.

Contribution

It introduces an alternative evaluation method for sinc integrals using combinatorial and geometrical perspectives, and explores their probabilistic interpretations.

Findings

New combinatorial/geometrical evaluation of sinc integrals

Probabilistic interpretation of sinc integrals and identities

Connections between integrals, combinatorics, and probability

Abstract

We give an alternative, combinatorial/geometrical evaluation of a class of improper sinc integrals studied by the Borweins. A probabilistic interpretation is also noted and used to shed light on a related combinatorial identity.