This function computes the Hankel transform defined as integral from 0 to inf f(x, dstruct) J sub order (x r) dx, where J sub order is a Bessel function of the first kind and order is either 0 or 1. The variable dstruct is a structure to pass data to f the (possibly) complex user provided function f. The variables rerr and aerr are the relative and absolute error passed to the Matlab function integral.
The algorithm used is integration between the zero crossings of the Bessel function to obtain partial integrals, followed by their summation using the Padé approximants. This approach is generally more accurate than digital filter algorithms. It also is able to handle well defined but divergent integrals such as f(x) = x.