我们在本文中研究非紧致一秩Ｒｉｅｍａｎｎ对称空间上初等球函数的渐近表示，并利用Ｌｏｈｏｕｅ Ｎ．和Ｒｙｃｈｎｅｒ Ｔｈ．得到的热核表达式，建立起这类空间上的非欧中心极限定理，所得结果包含了Ｔｅｒｒａｓ的定理作为其特例．

in this paper, we investigate the asymptotic expressions of the elementary spherical functions on the non-compact Riemannian symmetric spaces of ranks one, and use the heat kernel obtained by Lohoue and Rychner to establish the central limit theorem for these spaces, our conclusion includes Terras theorem as a special case.