ASYMPTOTIC EXPANSIONS OF SOME MATRIX ARGUMENT HYPERGEOMETRIC FUNCTIONS, WITH APPLICATIONS

TO MACROMOLECULES

GAOYUAN WEI AND B. E. EICHINGER

Department of Chemistry, BG-10, University of Washington, Seattle, WA 98195, U.S.A.

(Received October 30, 1990; revised July 16, 1991)

Abstract. We have studied the asymptotics of two special two-matrix hypergeometric functions. The validity of the asymptotic expressions for these functions is seen in several selected numerical comparisons between the exact and asymptotic results. These hypergeometric functions find applications in configuration statistics of macromolecules as well as multivariate statistics.

Key words and phrases: Asymptotics, hypergeometric functions of matrix argument, Wishart distribution, macromolecule size and shape distribution functions.