English

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

R2 v1 2026-06-28T09:39:09.368Z