Some applications of the Poisson summation formula

TL;DR

This paper develops specialized forms of the Poisson summation formula for even and odd functions, enabling new representations of Euler-type numbers and summation of series connected to elliptic functions.

Contribution

It introduces new variants of the Poisson summation formula tailored for even and odd functions, with applications to Euler numbers and elliptic series.

Findings

Derived specialized Poisson summation formulas for even and odd functions.

Obtained new representations for Euler-type numbers.

Summed series related to elliptic functions.

Abstract

We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.