Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument |
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Authors: | Richards Donald St P |
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Institution: | 1. Department of Statistics, Penn State University, University Park, Pennsylvania, 16802-2111
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Abstract: | In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0 F 1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0 F 1functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( r F s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP2properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson Lewis Carroll] (1866). |
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