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Algorithms and codes for the Macdonald function: Recent progress and comparisons. (English) Zbl 1033.65010
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:
65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, 0 F 1
44A15Special transforms (Legendre, Hilbert, etc.)
65R10Integral transforms (numerical methods)
33F05Numerical approximation and evaluation of special functions