A remark on Algorithm 644: “A portable package for Bessel functions of a complex argument and nonnegative order”

ABSTRACT

Algorithm 644 computes all major Bessel functions of a complex argument and of nonnegative order. Single-precision routine CBESY and double-precision routine ZBESY are modified to reduce the computation time for the Y Bessel function by approximately 25% over a wide range of arguments and orders. Quick check (driver) programs that exercise the package are also modified to make tests more meaningful over larger regions of the complex plane.

REFERENCES

• 1: ABRAMOWlTZ, M. AND STEGUN, I.A. 1995. Handbook of Mathematical Functions. NBS Applied Math Series, vo}. 55. U.S. Dept. of Commerce, Washington, D.C.
• 2: D. E. Amos, ALGORITHM 644: a portable package for Bessel functions of a complex argument and nonnegative order, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.265-273, Sept. 1986 [doi>10.1145/7921.214331]
• 3: D. E. Amos, Remark on algorithm 644, ACM Transactions on Mathematical Software (TOMS), v.16 n.4, p.404, Dec. 1990 [doi>10.1145/98267.98299]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms

Keywords:
H, I, J, K, and Y Bessel functions, complex Airy functions, complex Bessel functions, derivatives of Airy functions, log gamma function