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Partial differential equations for hypergeometric functions of two argument matrices

Author

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  • Constantine, A. G.
  • Muirhead, R. J.

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.

Suggested Citation

  • Constantine, A. G. & Muirhead, R. J., 1972. "Partial differential equations for hypergeometric functions of two argument matrices," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 332-338, September.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:3:p:332-338
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    Citations

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    Cited by:

    1. Javier Ibáñez & José M. Alonso & Jorge Sastre & Emilio Defez & Pedro Alonso-Jordá, 2021. "Advances in the Approximation of the Matrix Hyperbolic Tangent," Mathematics, MDPI, vol. 9(11), pages 1-20, May.
    2. Yasuko Chikuse, 1976. "Partial differential equations for hypergeometric functions of complex argument matrices and their applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 187-199, December.
    3. Ghazi S. Khammash & Praveen Agarwal & Junesang Choi, 2020. "Extended k-Gamma and k-Beta Functions of Matrix Arguments," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    4. Ahmed Bakhet & Fuli He, 2020. "On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals," Mathematics, MDPI, vol. 8(2), pages 1-12, February.

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