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Zbl 1072.65024
Gil, Amparo; Segura, Javier; Temme, Nico M.
Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments. (English)
[J] ACM Trans. Math. Softw. 30, No. 2, 145-158 (2004). ISSN 0098-3500

Summary: We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w''+ xw'+ (a^2- x^2)w = 0$. In the accompanying paper [ibid. 30, No.~2, 159--164 (reviewed below)], we describe the implementation of these methods in Fortran 77 codes.

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33F05 Numerical approximation of special functions
65Y15 Packaged methods

Keywords: modified Bessel functions; derivatives; Fortran 77 codes

Citations: Zbl 1072.65023

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