Products of Bessel functions and associated polynomials

Abstract

Symbolic methods of umbral nature are exploited to derive series expansion for the products of Bessel functions. It is shown that the product of two cylindrical Bessel functions can be written in terms of Jacobi polynomials. The procedure is extended to products of an arbitrary number of functions and the link with previous researchers is discussed. We show that the technique we propose and the use of the Ramanujan master theorem allow the derivation of integrals of practical interest.