Bessel Systems for Jordan Algebras of Rank 2 and 3

Special functions of matrix argument arise in a diverse range of applications in harmonic analysis, number theory, multivariate statistics, quantum physics, and molecular chemistry. This paper presents series expansions for the Bessel functions associated with Jordan algebras of rank 2 or 3. Detailed information on the domains of convergence of these series are given where Horn’s theorems for double and triple hypergeometric series are used.