Abstract :
A standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument,
and to use an asymptotic series for large argument; with the choice of the series changing at some appropriate argument magnitude,
depending on the number of digits required. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [D. Borwein, J.M. Borwein,
R. Crandall, Effective Laguerre asymptotics, preprint at http://locutus.cs.dal.ca:8088/archive/00000334/] 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 provide a viable alternative to the conventional ascendingasymptotic
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.
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