Algorithm 794: numerical Hankel transform by the Fortran program HANKEL

ABSTRACT

The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.

REFERENCES

• 1: Walter L. Anderson, Fast Hankel Transforms Using Related and Lagged Convolutions, ACM Transactions on Mathematical Software (TOMS), v.8 n.4, p.344-368, Dec. 1982 [doi>10.1145/356012.356014]
• 2: COURANT, R. AND HILBERT, D. 1968. Methoden der Mathematischen Physik. Springer-Verlag, Berlin, Germany.
• 3: ERDELYI, A., MAGNUS, W., OBERHETTINGER, F., AND TRICOMI, F. 1954. Tables of Integral Transforms. McGraw-Hill, Inc., New York, NY.
• 4: KORN, A. AND KORN, T. 1968. Mathematical Handbook for Scientists and Engineers. McGraw-Hill, Inc., New York, NY.
• 5: James Lyness , Gwendolen Hines, ALGORITHM 639: to integrate some infinite oscillating tails, ACM Transactions on Mathematical Software (TOMS), v.12 n.1, p.24-25, March 1986 [doi>10.1145/5960.214318]
• 6: PIESSENS, R. 1982. Automatic computation of Bessel function integrals. Comput. Phys. Commun. 25, 289.
• 7: SIEGMAN, A. 1980. Quasi fast Hankel transform. Opt. Lett. 1, 13-15.
• 8: K. Sikorski , F. Stenger , J. Schwing, Algorithm 614: a FORTRAN subroutine for numerical integration in H(sub)p, ACM Transactions on Mathematical Software (TOMS), v.10 n.2, p.152-157, June 1984 [doi>10.1145/399.449]
• 9: SNEDDON, I. 1955. Functional Analysis. In Handbuch der Physik, S. Flugge, Ed. Springer-Verlag, Berlin, Germany.
• 10: WATERLOO MAPLE. 1996. Maple. (Software). Waterloo Maple, Inc., Waterloo, Ontario, Canada. http://www.maplesoft.com
• 11: TALMAN, g. 1983. Lsfbtr: A subroutine for calculating spherical bessel transforms. Comput. Phys. Commun. 30, 93.
• 12: WHITTAKER, E. AND WATSON, G. 1978. Modern Analysis. Cambridge University Press, New York, NY.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN 77

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computation of transforms (e.g., fast Fourier transform)

General Terms:
Algorithms

Keywords:
Hankel transform, numerical analysis