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We describe a variety of methods to compute the functions Kia(x), Lia(x) and their derivatives for real a and positive x. These functions are numerically satisfactory independent solutions of the differential equation x2 w" + xw' + (a2 − x2)w = 0. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.

Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments