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

## Abstract:

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.
## Bibtex entry:

@INPROCEEDINGS{harrison-bessel,
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"}