Algorithms and codes for the Macdonald function: recent progress and comparisons

The modified Bessel function K i ν ( x), also known as the Macdonald function, finds application in the Kontorovich–Lebedev integral transform when x and ν are real and positive. In this paper, a comparison of three codes for computing this function is made. These codes differ in algorithmic approac...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 161; no. 1; pp. 179 - 192
Main Authors: Fabijonas, B.R., Lozier, D.W., Rappoport, J.M.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2003
Subjects:
Bessel functions
Computation of special functions
Macdonald functions
Computation of special functions
Bessel functions
Macdonald functions
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The modified Bessel function K i ν ( x), also known as the Macdonald function, finds application in the Kontorovich–Lebedev integral transform when x and ν 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.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(03)00596-X