Evaluation of first-order Hankel transforms using Filon quadrature philosophy Original Research Article

An algorithm for evaluating first-order Hankel transforms using Filon quadrature philosophy is presented. In Filon quadrature philosophy, the integrand is separated into the product of an (assumed) slowly varying component and a rapidly oscillating component. The former, in the present problem, is h(p)p and the latter is J1(rp) (see equation (1.2)). Only h(p)p is approximated in the basic subinterval, instead of the entire integrand being approximated. Since only h(p)p has to be approximated, only a relatively small number of subintervals is needed. In addition, the error incurred is relatively independent of the magnitude of r.