Fast and Accurate Bessel Function Computation

John Harrison.

Proceedings of ARITH19, the 19th IEEE Conference on Computer Arithmetic, IEEE Computer Society Press, 2009, pp. 104-113.


The Bessel functions are considered relatively difficult to compute. Although they have a simple power series expansion that is everywhere convergent, they exhibit approximately periodic behavior which makes the direct use of the power series impractically slow and numerically unstable. We describe an alternative method based on systematic expansion around the zeros, refining existing techniques based on Hankel expansions, which mostly avoids the use of multiprecision arithmetic while yielding accurate results.

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Bibtex entry:

        author          = "John Harrison",
        title           = "Fast and Accurate {B}essel Function Computation",
        editor          = "Javier D. Bruguera and Marius Cornea and
                           Debjit DasSarma and John Harrison",
        booktitle       = "Proceedings of the 19th IEEE Sympoisum on
                           Computer Arithmetic",
        address         = "Portland OR",
        publisher       = "IEEE Computer Society",                   
        year            = 2009,
        pages           = "104--113"}