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 xf(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 xf(x), thereby getting an efficient algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm.