Numerical evaluation of Hankel transforms via Gaussian-Laguerre polynomial expansions

Hankel transforms of individual members of the orthonormal set of Gaussian-Laguerre (G-L) functions yield the same functional form as the original members. Thus, the Hankel transform of arbitrary functions can be accomplished in principle by expanding the function into G-L functions and using the same expansion coefficients for calculating the Hankel transformation. Numerical evaluation for the circular function illustrates the convergence features of this type of expansion.