Filon trapezoidal schemes for Hankel transforms of orders zero and one

Algorithms for evaluating zero-order and first-order Hankel transforms using Filon quadrature philosophy are developed in the context of a trapezoidal approximation rather than of a Simpsonʹs rule approximation previously discussed. Unlike the Filon/Simpson algorithm previously developed, the Filon/trapezoidal algorithm tends to saturate, in that increasing the number of quadrature points does not materially increase the accuracy. Numerical examples are given and discussed.