Efficient algorithms to compute Hankel transforms using wavelets

The aim of the paper is to propose two efficient algorithms for the numerical evaluation of Hankel transform of order ν, ν>−1 using Legendre and rationalized Haar (RH) wavelets. The philosophy behind the algorithms is to replace the part xf(x) of the integrand by its wavelet decomposition obtained by using Legendre wavelets for the first algorithm and RH wavelets for the second one, thus representing Fν(y) as a Fourier-Bessel series with coefficients depending strongly on the input function xf(x) in both the cases. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithms.