A fast algorithm for computing the Hankel transform of order 1

A fast algorithm for computing the Hankel transform of order one is derived by slightly modifying the algorithm developed by E.W. Hansen (1985). Since the algorithm uses the formal equivalency between a Hankel transform and an Abel transform followed by a Fourier transform, it enjoys computational advantages using a rapid Abel transform with shift-variant recursive filter and a fast Fourier transform. Good agreement between actual and computer transforms was obtained in the simulation with a known transform pair