Rapidly convergent series and closed-form expressions for a class of integrals involving products of spherical Bessel functions

Rapidly convergent series are derived to efficiently evaluate a class of integrals involving the product of spherical Bessel functions of the first kind occurring in acoustic and electromagnetic scattering from circular disks and apertures. Depending on the involved parameters, the series can be further reduced to closed-form expressions in terms of generalized hypergeometric functions or Meijer G-functions, which can immediately be evaluated through current mathematical toolboxes. Numerical results are provided showing that the accuracy of the series representation can easily be controlled and that the proposed solutions are at least 1000 times faster than specific quadrature schemes which, in general, have to deal with irregularly oscillating and slowly decaying functions.