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

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

2004-01-13

arxiv.org/abs/math/0401128v1

Mathematics

Numerical Analysis

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

Scientific paper

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 $x^2 w'' +x w' +(a^2 -x^2)w=0$. 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.

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