An improved method for computing Hankel transform

Abstract

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 sqrt(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 sqrt(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. © 2008 The Franklin Institute.