- Title
- The evaluation of Bessel functions via exp-arc integrals
- Creator
- Borwein, David; Borwein, Jonathan M.; Chan, O-Yeat
- Relation
- Journal of Mathematical Analysis and Applications Vol. 341, Issue 1, p. 478 - 500
- Publisher Link
- http://dx.doi.org/10.1016/j.jmaa.2007.10.003
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2008
- Description
- 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.
- Subject
- Bessel function; uniform series expansion; exponential-hyperbolic expansions
- Identifier
- http://hdl.handle.net/1959.13/927020
- Identifier
- uon:10019
- Identifier
- ISSN:0022-247X
- Language
- eng
- Full Text
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