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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
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A Reflection Formula for the Gaussian Hypergeometric Function of Matrix Argument
, 2020 We obtain a reflection formula for the Gaussian hypergeometric function of real symmetric matrix argument. We also show that this result extends to the Gaussian hypergeometric function defined over the symmetric cones, and even to generalizations of the ...
Donald Richards, Qifu Zheng
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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
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
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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
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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
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
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Gevrey expansions of hypergeometric integrals II
, 2019 We study integral representations of the Gevrey series solutions of irregular hypergeometric systems under certain assumptions. We prove that, for such systems, any Gevrey series solution, along a coordinate hyperplane of its singular support, is the ...
Castro-Jiménez, Francisco-Jesús +2 more
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, 2008 We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Z^d-graded binomial ideal I along with Euler operators defined by the grading and a parameter in C^d. We determine the parameters for which these D-modules (i)
Dickenstein, Alicia +2 more
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Advanced Biology, EarlyView.The axolotl's remarkable regenerative abilities decline with age, the causes may include the numerous repetitive elements within its genome. This study uncovers how Ty3 retrotransposons and coexpression networks involving muscle and immune pathways respond to aging and regeneration, suggesting that transposons respond to physiological shifts and may ...
Samuel Ruiz‐Pérez +8 more
wiley +1 more source