Evaluation of some algorithms and programs for the computation of integer-order Bessel functions of the first and second kind with complex arguments

The efficiency and accuracy of a few available algorithms for the computation of integer-order Bessel functions are considered. First, the computation of integer-order Bessel functions of the first kind, using the fast Fourier transform (FFT) algorithm as opposed to recurrence techniques, is investigated. It is shown that recurrence techniques are superior to the FFT technique, both in accuracy and speed. An algorithm suggested in the literature and used in commercially available software, specifically MATLAB 3.5 and MATHEMATICA 1.2, for computing integer-order Bessel functions of the second kind is revealed to be erroneous by comparing these routines with an algorithm developed by the author. It is shown that catastrophic errors result from using the erroneous algorithm to compute high-order Bessel functions with nonreal arguments.<>