Algorithm 877

Author:

Kodama Masao

Abstract

The algorithm presented provides a package of subroutines for calculating the cylindrical functions J ν ( x ), N ν ( x ), H ν (1) ( x ), H ν (2) ( x ) where the order ν is complex and the real argument x is nonnegative. The algorithm is written in Fortran 95 and calculates the functions using single, double, or quadruple precision according to the value of a parameter defined in the algorithm. The methods of calculating the functions are based on a series expansion, Debye's asymptotic expansions, Olver's asymptotic expansions, and recurrence methods (Miller's algorithms). The relative errors of the functional values computed by this algorithm using double precision are less than 2.4×10  − 13 in the region 0 ≤ Re ν  ≤ 64, 0 ≤ Im ν  ≤ 63, 0.024 ≤  x  ≤ 97.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Reference29 articles.

1. Amos D. E. 1983a. Computation of Bessel functions of complex argument. Tech. rep. SAND83--0086 Sandia National Laboratories. Amos D. E. 1983a. Computation of Bessel functions of complex argument. Tech. rep. SAND83--0086 Sandia National Laboratories.

2. Amos D. E. 1983b. Computation of Bessel functions of complex argument and large order. Tech. rep. SAND83--0643 Sandia National Laboratories. Amos D. E. 1983b. Computation of Bessel functions of complex argument and large order. Tech. rep. SAND83--0643 Sandia National Laboratories.

3. Char B. W. Geddes K. O. Gonnet G. H. Leong B. L. Monagan M. B. and Watt S. M. 1991. Maple V Library Reference Manual. Springer-Verlag Berlin Germany. Char B. W. Geddes K. O. Gonnet G. H. Leong B. L. Monagan M. B. and Watt S. M. 1991. Maple V Library Reference Manual . Springer-Verlag Berlin Germany.

4. Algorithm 838

5. Felsen L. B. and Marcuvitz N. 1994. Radiation and Scattering of Waves. IEEE Press Los Alamitos CA 323--328. Felsen L. B. and Marcuvitz N. 1994. Radiation and Scattering of Waves . IEEE Press Los Alamitos CA 323--328.

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