Algorithm 877: A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument

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.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE

General Terms:
Algorithms

Keywords:
Cylindrical functions, complex order, nonnegative argument, numerical calculation