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

ABSTRACT

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 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.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE

General Terms:
Algorithms

Keywords:
Bessel functions, asymptotic expansions, numerical quadrature