Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions
We present an algorithm to compute integrals of the form [GRAPHICS] with J(vi)(x) the Bessel function of the first kind and (real) order v(i). The parameter m is a real number such that Sigma(i) v(i) + m > -1 and the coefficients ai are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for J(vi)(x) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Gamma(a, z). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.
algorithms bessel functions quadrature