Fast and Accurate Bessel Function Computation

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.

• Type: Conference
• Year: 2009
• Where: ARITH
• Authors: John Harrison
• Keywords: Applied Computing, ARITH 2009, Bessel Functions, Power Series Expansion, Systematic Expansion