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Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for the occasion.
The Bessel-Muirhead hypergeometric system (or 0 F 1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients , in order to express the K-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed. 1.… (More)
Bessel functions of matrix argument appeared as a subject of studies in the work of Herz . One can find in the multivariate statistics literature some applications of these functions (see ). 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”… (More)