Numerical evaluation of the Hankel transform by using linear Legendre multi-wavelets
An efficient algorithm for evaluating the Hankel transform Fn(p) F n ( 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) L 2 ( R ) ; we expand the part rf(r) 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.
hankel transform linear legendre multi-wavelets bessel functions sombrero function