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The evaluation of Bessel functions via exp-arc integrals

Borwein, David and Borwein, Jonathan M. and Chan, O-Yeat (2008) The evaluation of Bessel functions via exp-arc integrals. Journal of Mathematical Analysis and Applications, 341 (1). 478 - 500.

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    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 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.

    Item Type: Article
    Uncontrolled Keywords: Bessel function, uniform series expansion, exponential-hyperbolic expansions
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 11 Jan 2015 17:58
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1231

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