Evaluating infinite integrals involving products of Bessel functions of arbitrary order

The difficulties involved with evaluating infinite integrals involving products of Bessel functions are considered, and a method for evaluating these integrals is outlined. The method makes use of extrapolation on a sequence of partial sums, and requires rewriting the product of Bessel functions as the sum of two more well-behaved functions. Numerical results are presented to demonstrate the efficiency of this method, where it is shown to be significantly superior to standard infinite integration routines.