Laplace Transform of Products of Bessel Functions: A Visitation of Earlier Formulas

Abstract

This note deals with the Laplace transforms of integrands of the form $ {x^\lambda }{J_\alpha }\left( {ax} \right){J_\beta }\left( {bx} \right)$, which are found in numerous fields of application. Specifically, we provide herein both a correction and a supplement to the list of integrals given in 1997 by Hanson and Puja, who in turn extended the formulas of Eason, Noble and Sneddon of 1956. The paper concludes with an extensive tabulation for particular cases and range of parameters.