Evaluation of some algorithms and programs for the computation of integer-order Bessel functions of the first and second kind with complex arguments
The purpose of this article is to provide some insight on the efficiency and accuracy of a few available algorithms for the computation of integer-order Bessel functions. First, the computation of integer-order Bessel functions of the first kind (Jn(z)), 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 efficiency. Second, an erroneous algorithm, suggested in the literature and used by commercially available software, specially MATLAB 3.5 and MATHEMATICA 1.2, for computing integer-order Bessel functions of the second kind (Yn(z)), is revealed by comparing these routines with an algorithm developed by the author. Catastrophic errors result from the use of the erroneous algorithm, for the computation of large orders with non-real arguments.