SIAM Journal on Mathematical Analysis
The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Algorithms and codes for the Macdonald function: recent progress and comparisons
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Algorithm 831: Modified Bessel functions of imaginary order and positive argument
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Zeros of the Macdonald function of complex order
Journal of Computational and Applied Mathematics
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)
Hi-index | 31.45 |
The evaluation of the modified Bessel function of the third kind of purely imaginary order Kia(x) is discussed; we also present analogous results for the derivative. The methods are based on the use of Maclaurin series, nonoscillatory integral representations, asymptotic expansions, and a continued fraction method, depending on the ranges of x and a. We discuss the range of applicability of the different approaches considered and conclude that power series, the continued fraction method, and the nonoscillatory integral representation can be used to accurately compute the function Kia(x) in the range 0 ≤ a ≤ 200, 0 ≤ x ≤ 100; using a similar scheme the derivative K'ia(x) can also be computed within these ranges.