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

An efficient algorithm for evaluating the Hankel transform Fn(p)Fn(p) of order n   of a function f(r)f(r) is given. As the continuous Legendre multi-wavelets forms an orthonormal basis for L2(R)L2(R); we expand the part rf(r)rf(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.