A Septuple Integral of the Product of Three Bessel Functions of the First Kind Jα(tβ)Jγ(xδ)Jη(yθ): Derivation and Evaluation over General Indices

Abstract

Closed expressions for a number of septuple integrals involving the product of three Bessel functions of the first kind Jα(tβ)Jγ(xδ)Jη(yθ) when the orders α,γ,η are large, are derived in terms of the Hurwitz–Lerch zeta function Φ(z,s,v). The integrals are not easy to to evaluate for complex values of the parameters. All the results in this work are new.