Fast Nth-order Hankel transform algorithm

An Nth-order Hankel transform (also called Fourier-Bessel transform) algorithm designed for many analytically defined functions is presented. This algorithm is not restricted to order zero. As such, it provides greater generality than many others. The traditional difficulty in the evaluation of Hankel transforms, the presence of Bessel functions in the kernel of the integral transform, is eliminated in this new Hankel transform algorithm. The algorithm presented is composed of a fast (linear time) Nth-order Chebyshev transform followed by a fast Fourier transform