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Algorithms and Codes for the Macdonald Function: Recent Progress and Comparisons



B R. Fabijonas, Daniel W. Lozier, J M. Rappoport


The modified Bessel function Kχ, also known as the Macdonald function, finds application in the Kontorovich-Lebedev integral transform when χ and Ņ 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 independently of the other two through Wronskian checks, and therefore is used as a standard against which the others are compared.
NIST Interagency/Internal Report (NISTIR) - 6596
Report Number


Bessel functions, computation of special functions, Macdonald function


Fabijonas, B. , Lozier, D. and Rappoport, J. (2003), Algorithms and Codes for the Macdonald Function: Recent Progress and Comparisons, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD (Accessed June 24, 2024)


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Created January 31, 2003, Updated October 12, 2021