Sums of products of Bessel functions and order derivatives of Bessel functions

TL;DR

This paper investigates sums involving Bessel functions, deriving new expressions in terms of Bessel functions and their integrals, which can be represented as Meijer G functions, enhancing analytical tools for special functions.

Contribution

The paper introduces novel formulas for sums of Bessel functions expressed through Bessel functions, their integrals, and Meijer G functions, expanding existing mathematical frameworks.

Findings

Derived expressions for sums of Bessel functions in terms of Bessel functions and integrals

Expressed integrals as Meijer G functions for broader applicability

Provided analytical tools for advanced studies of special functions

Abstract

In this paper, sums represented in (3) are studied. The expressions are derived in terms of Bessel functions of the first and second kinds and their integrals. Further, we point out the integrals can be written as a Meijer G function.