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

Abstract

An efficient algorithm for evaluating the Hankel transform F n ( p ) of order n of a function f ( r ) is given. As the continuous Legendre multi-wavelets forms an orthonormal basis for L 2 ( 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.