More remarkable sinc integrals and sums

TL;DR

This paper employs the Poisson summation formula to evaluate integrals involving sinc functions, generalizes previous results, introduces new remarkable integrals, and presents a sum version of a Siegel-type lower bound.

Contribution

It introduces new integrals related to sinc functions, generalizes existing results, and provides a sum version of a Siegel-type lower bound, expanding the mathematical understanding of these integrals.

Findings

Calculated integrals of sinc function products using Poisson summation

Generalized previous sinc integral results and introduced new integrals

Presented a sum version of a Siegel-type lower bound

Abstract

We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum version of Siegel-type lower bound. (cf. [2], Theorem 3)