On the evaluation of the integral over the product of two spherical Bessel functions

The integral I(l,l')(k,k') = integral-o-infinity-j(l')(kr)j(l') (k'r)r2 dr, in which the sperical Bessel functions j(l)(kr) are the radial eigenfunctions of the three-dimensional wave equation in spherical coordinates, is evaluated in terms of distributions, in particular, step functions and delta functions. It will be shown that the behavior of I(l,l') is very different in the cases l - l' even (0, +/- 2, +/- 4,...) and l - l' odd (+/- 1, +/- 3, ...). For l - l' even it is expressed in terms of the delta function, step functions, and Legendre polynomials. For l - l' odd it is expressed in terms of Legendre functions of the second kind and step functions; no delta functions appear.