Results 11 to 20 of about 2,765,689 (216)
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
semanticscholar +4 more sources
Extended k-Gamma and k-Beta Functions of Matrix Arguments
Mathematics, 2020 Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented ...
Ghazi S. Khammash +2 more
doaj +2 more sources
Journal of Multivariate Analysis, 2015 This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a central Wishart ensemble with fixed-rank perturbation of the identity matrix, the second is a non-central Wishart
Passemier, Damien +2 more
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Laplace approximations to hypergeometric functions of two matrix arguments
Journal of Multivariate Analysis, 2005 AbstractWe present a unified approach to Laplace approximation of hypergeometric functions with two matrix arguments. The general form of the approximation is designed to exploit the Laplace approximations to hypergeometric functions of a single matrix argument presented in Butler and Wood (Ann. Statist. 30 (2002) 1155, Laplace approximations to Bessel
Andrew T. A. Wood, Ronald W. Butler
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Expressions for some hypergeometric functions of matrix argument with applications
Journal of Multivariate Analysis, 1975 AbstractReasonably simple expressions are given for some hypergeometric functions when the size of the argument matrix or matrices is two. Applications of these expressions in connection with the distributions of the latent roots of a 2 × 2 Wishart matrix are also given.
Robb J. Muirhead
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High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument [PDF]
Symmetry, 2011 Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups.
Donald St. P. Richards
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Total positivity, spherical series, and hypergeometric functions of matrix argument
Journal of Approximation Theory, 1989 AbstractGiven a totally positive function K of two real variables, is there a method for establishing the total positivity of K in an “obvious” fashion? In the case in which K(x, y) = f(xy), where f is real-analytic in a neighborhood of zero, we obtain integral representations for the determinants which define the total positivity of K.
Kenneth I. Gross, St. P. Richards
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Eigenvalue distributions of beta-Wishart matrices [PDF]
, 2018 We derive explicit expressions for the distributions of the extreme eigenvalues of the Beta-Wishart random matrices in terms of the hypergeometric function of a matrix argument. These results generalize the classical results for the real (β = 1), complex
Edelman, Alan, Koev, Plamen S
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The Efficient Evaluation of the Hypergeometric Function of a Matrix Argument [PDF]
arXiv, 2005 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, A. Edelman
arxiv +3 more sources
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
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