Application of the Wavelet Transform with a Piecewise Linear Basis to   the Evaluation of the Hankel Transform
  A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a basis such that its scalar product with the Bessel function is calculated analytically. The result is represented as a series, with the coefficients strongly depending on the local behavior of the function being transformed. The application of the method is demonstrated by an example illustrated with plots. 
P. S. Zykov, E. B. Postnikov