Coulomb and Bessel functions of complex arguments and order
Journal of Computational Physics
Fortran 90/95 explained (2nd ed.)
Fortran 90/95 explained (2nd ed.)
Complex gamma function with error control
Communications of the ACM
Evaluation of the modified Bessel function of the third kind of imaginary orders
Journal of Computational Physics
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
The Mathematica Book
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Algorithm 912: A Module for Calculating Cylindrical Functions of Complex Order and Complex Argument
ACM Transactions on Mathematical Software (TOMS)
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The algorithm presented provides a package of subroutines for calculating the cylindrical functions Jν(x), Nν(x), Hν(1)(x), Hν(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.