Results 1 to 10 of about 2,765,689 (216)
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
core +8 more sources
A reflection formula for the Gaussian hypergeometric function of matrix argument [PDF]
Journal of Mathematical Analysis and Applications, 2020 11 ...
Richards, Donald, Zheng, Qifu
core +8 more sources
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.
Alan Edelman, Plamen Koev
core +8 more sources
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.
Yifeng Xue, Fei Li
arxiv +7 more sources
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 ...
Butler, Roland W., Wood, Andrew T. A.
semanticscholar +5 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
openaire +4 more sources
Hypergeometric Functions of 2 × 2 Matrix Argument are Expressible in Terms of Appell's Functions F 4 [PDF]
Proceedings of the American Mathematical Society, 1978 It is proved that the hypergeometric function of 2 × 2 2 \times 2 matrix argument is expressible as a solution of the partial differential equations for Appell’s function F 4 {F_4} . As a result the first-mentioned function can be written as a sum of two
Tom H. Koornwinder +1 more
+5 more sources
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
+5 more sources
Journal of Multivariate Analysis, 2021 This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the derivation of certain distributions for the eigenvalues of singular beta-Wishart matrices.
Koki Shimizu, Hiroki Hashiguchi
+7 more sources
Special Functions of Matrix Argument. I: Algebraic Induction, Zonal Polynomials, and Hypergeometric Functions [PDF]
Transactions of the American Mathematical Society, 1987 Hypergeometric functions of matrix argument arise in a diverse range of applications in harmonic analysis, multivariate statistics, quantum physics, molecular chemistry, and number theory. This paper presents a general theory of such functions for real division algebras.
Donald St. P. Richards, Kenneth I. Gross
+4 more sources