Hypergeometric Functions Associated to Cones of Convex Type in a Euclidean Jordan Algebra

In this paper, we study a family of hypergeometric functions associated to cones of convex type in a Euclidean Jordan algebra. We obtain upper and lower bounds and give information about their singularities. The family under consideration was introduced by Sahi (Invent. Math.110 (1992), 409–418) and it plays an important role in the construction of some small representations.