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.
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