Algorithm 858

Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions. We present an algorithm to compute integrals of the form ∫∞0 xm ∏ki = 1Jνi(aix)dx with Jνi(x) the Bessel function of the first kind and (real) order νi. The parameter m is a real number such that ∑i νi + m > −1 and the coefficients ai are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for Jνi(x) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Γ(a,z). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.

This software is also peer reviewed by journal TOMS.