NUMERICAL EVALUATION OF THE ZERO-ORDER HANKEL TRANSFORM USING FILON QUADRATURE PHILOSOPHY

The purpose of this communication is to present an algorithm for evalu ating zero-order Hankel tranforms using ideas first put foward by Filo n in the context of finite range Fourier integrals. In Filon quadratur e philosophy, the integrand is separated into the product of an (assum ed) slowly varying component and a rapidly oscillating one (in our pro blem, the former is h(p) and the latter is J(0)(rp)p; see equation (1. 2). Here only h(p) is approximated by a quadratic over the basic subin terval instead of the entire integrand h(p)J(0)(rp)p being approximate d. Since only h(p) has to be approximated, only a relatively small num ber of subintervals is required. In addition, the error incurred is re latively independent of the magnitude of r. There is a profound differ ence between the finite range Fourier integral and the zero-order Hank el transform in that exp(irp) is periodic and translationally invarian t, whereas J(0)(rp) is an almost periodic decaying function.