An improved method for computing Hankel transform

The purpose of this paper is to compute the Hankel transform Fn(y) of order n of a function f(x) and its inverse transform using rationalized Haar wavelets. The integrand x f ( x ) is replaced by its wavelet decomposition. Thus representing Fn(y) as a Fourier–Bessel series with coefficients depending strongly on the local behavior of the function x f ( x ) , thereby getting an efficient algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm.