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 $x^2{w}^{\prime \prime }+x{w}^{\prime }+(a^2-x^2)w=0$. In an accompanying paper (Algorithm xxx: Modified Bessel functions of imaginary order and positive argument) we describe the implementation of these methods in Fortran 77 codes.

14 pages, 1 figure. To appear in ACM T. Math. Soft