The Evaluation of Bessel Functions via Exp-arc Integrals
نویسندگان
چکیده
The standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument |z|, and to use an asymptotic series for large |z|. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [1] derived a series for an exp-arc integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such series can be rapidly evaluated via recursion and elementary operations, and provides a viable alternative to the conventional ascending-asymptotic switching. In the present work, we extend the method to deal with Bessel functions of general (non-integral) order, as well as to deal with the Y and K Bessel functions. 2000 AMS Classi cation Numbers: 33C10 and 33F05.
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