An integral containing the product of four Bessel functions

TL;DR

This paper employs Mellin transform techniques to evaluate a complex integral involving four Bessel functions and a power, expressing the result through generalized hypergeometric functions.

Contribution

It introduces a novel Mellin transform approach to evaluate integrals of four Bessel functions, expanding the analytical tools available for such problems.

Findings

Integral expressed in terms of $_{6}F_{5}$ hypergeometric functions

Method provides a new way to evaluate similar integrals

Results extend existing integral tables and methods

Abstract

Mellin transform is used to evaluate an integral involving the product of four Bessel functions and a power. Using this method the result is obtained in terms of generalized hypergeometric functions $_{6}F_{5}$.