Fast and Accurate Bessel Function Computation

John Harrison
2009 2009 19th IEEE Symposium on Computer Arithmetic  
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
more » ... tic while yielding accurate results. • Evaluation near 0 for the singular Y n • Evaluation for 'small' arguments, roughly |x| < 45, but away from the singularities of the Y n at zero • Evaluation for 'large' arguments, roughly |x| ≥ 45.
doi:10.1109/arith.2009.32 dblp:conf/arith/Harrison09 fatcat:xnkcegcksbagzpmelsaoptuine