It is shown that the hypergeometric function of m × m scalar matrix argument (cf. Herz, Annals of Math., 61 (1955), pp. 474–523) may be expressed as the Pfaffian of a matrix whose entries are evaluated in terms of classical hypergeometric functions. Applications, in multivariate statistical theory, are made to the distributions of eigenvalues of various random matrices.
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Gupta et al. (1985) studied this question.
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