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The evaluation of Bessel functions via exparc integrals
 J. Math. Anal & Appl., accepted
, 2007
"... Abstract. A standard method for computing values of Bessel functions has been to use the wellknown 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 digit ..."
Abstract

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Abstract. A standard method for computing values of Bessel functions has been to use the wellknown 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 [1] derived a series for an “exparc ” 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 (nonintegral) order, as well as to deal with the Y and K Bessel functions.