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Zbl 1033.65010
Fabijonas, B. R.; Lozier, D. W.; Rappoport, J. M.
Algorithms and codes for the Macdonald function: Recent progress and comparisons. (English)
[J] J. Comput. Appl. Math. 161, No. 1, 179-192 (2003). ISSN 0377-0427

Summary: The modified Bessel function $K_{iv}(x)$, also known as the Macdonald function, finds application in the Kontorovich-Lebedev integral transform when $x$ and $v$ are real and positive. In this paper, a comparison of three codes for computing this function is made. These codes differ in algorithmic approach, timing, and regions of validity. One of them can be tested independent of the other two through Wronskian checks, and therefore is used as a standard against which the others are compared.

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
44A15 Special transforms
65R10 Integral transforms (numerical methods)
33F05 Numerical approximation of special functions

Keywords: Macdonald functions; Bessel functions; Computation of special functions; Kontorovich-Lebedev integral transform

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