A new class of sum rules for products of Bessel functions

TL;DR

This paper introduces a new class of sum rules for products of Bessel functions, extending known properties and exploring physical applications, with comparisons to existing sum rules.

Contribution

It presents a novel class of sum rules for Bessel functions of the first kind, expanding mathematical tools and applications.

Findings

New sum rules for Bessel function products derived

Comparison with existing sum rules shows differences and similarities

Potential applications in physics discussed

Abstract

In this paper we derive a new class of sum rules for products of the Bessel functions of first kind. Using standard algebraic manipulations we extend some of the well known properties of $J_n$. Some physical applications of the results are also discussed. A comparison with the Newberger[J. Math. Phys. \textbf{23} (1982) 1278] sum rules is performed on a typical example.