Algebraic analysis of the hypergeometric function $$\,{_1F_{\!\!\;1}}\,$$ of a matrix argument [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2020 AbstractIn this article, we investigate Muirhead’s classical system of differential operators for the hypergeometric function $$\,{_1F_{\!\!\;1}}\,$$ 1
Paul Görlach +2 more
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A reflection formula for the Gaussian hypergeometric function of matrix argument [PDF]
Journal of Mathematical Analysis and Applications, 2023 11 ...
Donald Richards, Qifu Zheng
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The Efficient Evaluation of the Hypergeometric Function of a Matrix Argument [PDF]
Mathematics of Computation, 2005 We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions.
Plamen Koev, Alan Edelman
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Laplace approximations for hypergeometric functions with matrix argument [PDF]
The Annals of Statistics, 2002 In this paper we present Laplace approximations for two functions of matrix argument: the Type I confluent hypergeometric function and the Gauss hypergeometric function. Both of these functions play an important role in distribution theory in multivariate analysis, but from a practical point of view they have proved challenging, and they have acquired ...
Roland W. Butler, Andrew T. A. Wood
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Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications [PDF]
Hiroshima Mathematical Journal, 2007 In this paper we derive error bounds for asymptotic expansions of the hypergeometric functions ${}_1F_1(n; n+b; Z)$ and ${}_1F_1(n; n+b; -Z)$, where $Z$ is a $p \times p$ symmetric nonnegative definite matrix. The first result is applied for theoretical accuracy of approximating the moments of $\Lambda=|S_e|/|S_e+S_h|$, where $S_h$ and $S_e$ are ...
Yasunori Fujikoshi
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Zonal polynomials and hypergeometric functions of quaternion matrix argument [PDF]
Communications in Statistics - Theory and Methods, 2009 We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix $W\sim\mathbb{Q}W(n, )$, respectively.
Fei Li, Yifeng Xue
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The efficient evaluation of the hypergeometric function of a matrix argument [PDF]
Mathematics of Computation, 2006 We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have complexity that is only linear in the size of the matrix.
Plamen Koev, Alan Edelman
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New formulas of convolved Pell polynomials
AIMS Mathematics, 2023 The article investigates a class of polynomials known as convolved Pell polynomials. This class generalizes the standard class of Pell polynomials. New formulas related to convolved Pell polynomials are established.
Waleed Mohamed Abd-Elhameed +1 more
doaj +2 more sources
Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument [PDF]
The Annals of Mathematical Statistics, 1970 Many distributions in multivariate analysis can be expressed in a form involving hypergeometric functions $_pF_q$ of matrix argument e.g. the noncentral Wishart $(_0F_1)$ and the noncentral multivariate $F(_1F_1)$. For an exposition of distributions in this form see James [9].
Robb J. Muirhead
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Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument [PDF]
The Ramanujan Journal, 2010 We establish a positivity property for the difference of products of certain Schur functions, sλ(x), where λ varies over a fundamental Weyl chamber in ℝn and x belongs to the positive orthant in ℝn. Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions.
Donald St. P. Richards
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