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Numerical evaluation of the Hankel transform. (English) Zbl 1001.65138
Summary: A procedure for the numerical evaluation of the $n$th-order Hankel transform is presented. It is based on an extension of the zero-th-order algorithm proposed by S. M. Candel [An algorithm for the Fourier Bessel transform, Comput. Phys. Commun. 23, 343 (1981)]. 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.
##### MSC:
 65R10 Integral transforms (numerical methods) 44A15 Special transforms (Legendre, Hilbert, etc.)