Results 21 to 30 of about 2,765,689 (216)
Open Journal of Statistics, 2016 Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in ...
T. Pham-Gia, Dinh Ngoc Thanh
openaire +4 more sources
Fractional operators in the matrix variate case [PDF]
Fractional Calculus and Applied Analysis, 2013 Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in various problems of mathematics, statistics and natural sciences.
A. M. Mathai, H. Haubold
semanticscholar +2 more sources
Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems [PDF]
, 2020 Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions.
Rosengren, Hjalmar +1 more
core +2 more sources
The affinely invariant distance correlation [PDF]
, 2014 Sz\'{e}kely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Sz\'{e}kely and Rizzo (Ann. Appl. Statist. 3 (2009) 1236-1265), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets ...
Dueck, Johannes +3 more
core +1 more source
International Journal for Research in Applied Science and Engineering Technology, 2019 : In this chapter, we evaluated ten integrals associated with hypergeometric function of four variables of matrix argument with their statistical distribution. All the matrix involved were real positive definite symmetric of order m x m.
Pooja Singh
semanticscholar +1 more source
Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind [PDF]
SIGMA 17 (2021), 053, 33 pages, 2020 We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second kind by using a limit representation.
arxiv +1 more source
A new multivariable 6-psi-6 summation formula [PDF]
, 2006 By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived.
C. Krattenthaler +31 more
core +1 more source
On a matrix element representation of the GKZ hypergeometric functions [PDF]
, 2022 We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of non-reductive Lie algebras $\mathfrak{L}_N$ of oscillator type.
arxiv +1 more source
A study on Horn matrix functions and its confluent cases [PDF]
arXiv, 2022 In this paper, we give the matrix version of Horn's hypergeometric function and its confluent cases. We also discuss the regions of convergence, the system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions.
arxiv
Euler-type integrals for the generalized hypergeometric matrix function [PDF]
arXiv, 2023 In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.
arxiv