Partial differential equations for hypergeometric functions of two argument matrices

A. G. Constantine and R. J. Muirhead

Journal of Multivariate Analysis, 1972, vol. 2, issue 3, 332-338

Abstract: In multivariate analysis many of the noncentral latent root distributions can be expressed in terms of hypergeometric functions vFq of two-argument matrices. This paper is concerned with showing that the function 2F1(a, b; c; R, S) satisfies the partial differential equation where R1, R2,..., Rm and s1, s2,..., sm are the latent roots of the m - m symmetric matrices R and S, respectively. Differential equations for the 1F1, 0F1, 1F0 and 0F0 hypergeometric functions are also obtained. Useful applications of these differential equations will be considered in a later paper.

Keywords: Hypergeometric; functions; matrix; arguments; latent; roots (search for similar items in EconPapers)
Date: 1972
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Citations: View citations in EconPapers (4)

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