On the coefficients of an asymptotic expansion of spherical functions on symmetric spaces

Abstract

The asymptotic expansion of a spherical function on a symmetric space of noncompact type, obtained by HarishChandra, is a finite linear combination of expansions of the form (o, 'r,(0)e6-1. In this paper it is proved that limt,. , 'J'p(te-p) is finite and rational for any e, where is the restriction of half the sum of the positive roots.