Numerical evaluation of the Hankel transform by using linear Legendre multi-wavelets

Abstract

An efficient algorithm for evaluating the Hankel transform Fn (p) of order n of a function f (r) is given. As the continuous Legendre multi-wavelets forms an orthonormal basis for L2 (R); we expand the part r f (r) of the integrand in its wavelet series reducing the Hankel transform integral as a series of Bessel functions multiplied by the wavelet coefficients of the input function. Numerical examples are given to illustrate the efficiency of the proposed method. © 2008 Elsevier B.V. All rights reserved.