Procedures are described for the high-precision calculation of the modiied Bessel function K(x), 0 < < 1, and the Airy function Ai(x), for positive arguments x, as prerequisites for generating Gaussian quadrature rules having these functions as weight function.

Bessel functions of matrix argument appeared as a subject of studies in the work of Herz [6]. One can find in the multivariate statistics literature some applications of these functions (see [11]). The main tool of Herz’s work was the Laplace transform and its inverse in the space of real symmetric matrices. He obtained several properties but a “good” differential system was lacking. This was t...