On a Bessel function series related to the Riemann xi function
Classical Analysis and ODEs
2026-02-17 v4 Number Theory
Abstract
We establish new Fourier integral evaluations involving the Riemann xi function related to a series involving Bessel function of the first kind. We show this infinite series involving the Bessel function of the first kind solves a boundary value problem for the cylindrical heat equation.
Cite
@article{arxiv.2303.16423,
title = {On a Bessel function series related to the Riemann xi function},
author = {Alexander E. Patkowski},
journal= {arXiv preprint arXiv:2303.16423},
year = {2026}
}
Comments
Added to chapter 2, including a numerical example