Numerical evaluation of the Hankel transform Original Research Article

A procedure for the numerical evaluation of the nth-order Hankel transform is presented. It is based on an extension of the zeroth-order algorithm proposed by S. Candel. Using an integral representation of the Bessel function, a formula is derived for the transform as a weighted integral of the Fourier components of the input function. Unlike in previous algorithms for simultaneous evaluation of sets of transforms, in the proposed procedure the Hankel transform can be regarded as a coefficient of a Chebyshev expansion. This approach leads to a different numerical evaluation of the quadrature. Numerical evaluation of some test functions with known analytical Hankel transform illustrates the efficiency and accuracy of the proposed algorithm.