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

ABSTRACT

This algorithm is a package of subroutines for Computing Bessel functions Hv(1)(z), Hv(2)(z), Iv(z), Jv(z), Kv(z), Yv(z) and Airy functions Ai(z), Ai′(z), Bi(z), Bi′(z) for ordersv≥0 and complex z in −&pgr;<arg z≤&pgr;. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.

REFERENCES

• 1: ABRAMOWITZ, M., AND STEGUN, I.A. Handbook of Mathematical Functions, NBS Applied Math Series 55. U. S. Dept. of Commerce, Washington, D.C. 1955.
• 2: AMOS, D. E, Computation of Bessel functions of complex argument. SAND83-0086, Sandia National Laboratories, Albuquerque, N.M. (May 1983).
• 3: AMOS, D.E. Computation of Bessel functions of complex argument and large order. SAND83- 0643, Sandia National Laboratories, Albuquerque, N.M. (May 1983).
• 4: AMOS, D.E. A subroutine package for Bessel functions of a complex argument and nonnegative order. SAND85-1018, Sandia National Laboratories, Albuquerque, N.M. (May 1985).
• 5: CODY, W.J. Preliminary report on software for the modified Bessel functions of the first kind. Argonne National Laboratory Rep. TM 357, Argonne, Ill. (Aug. 1980).
• 6: Wayne R. Cowell, Sources and development of mathematical software, Prentice-Hall, Inc., Upper Saddle River, NJ, 1984
• 7: DORING, B. Complex zeros of cylinder functions. Math. Comput. 20, (1966), 215-222.
• 8: FONG, K. W., JEFFERSON, T. H., AND SUYEHIRO, T. Formal conventions of the SLATEC library. SIGNUM Newsl. 19, 1 (Jan. 1984), 17-22.
• 9: P. A. Fox , A. D. Hall , N. L. Schryer, Algorithm 528: Framework for a Portable Library [Z], ACM Transactions on Mathematical Software (TOMS), v.4 n.2, p.177-188, June 1978 [doi>10.1145/355780.355789]
• 10: JONES, R. E., AND KAHANER, D.K. XERROR, The SLATEC error-handlingpackage. SAND82- 0800, Sandia National Laboratories, Albuquerque, N. M. (May 1982).
• 11: SOOKNE, D.j. Bessel functions I and J of complex argument and integer order. NBS J. Res-B 77B (1973), 111-113.
• 12: SOOKNE, D.J. Certification of an algorithm for Bessel functions of complex argument. NBS J. Res-B 77B (1973), 133-136.

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 Bessel functions, complex airy functions, derivatives of airy functions, log gamma function