The Experts below are selected from a list of 41061 Experts worldwide ranked by ideXlab platform
Ramón Gutiérrez-jáimez - One of the best experts on this subject based on the ideXlab platform.
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Distributions of the compound and scale mixture of vector and spherical matrix variate elliptical distributions
Journal of Multivariate Analysis, 2011Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-jáimezAbstract:Several matrix variate Hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted Hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted Hypergeometric type distributions is also derived as a particular case of the compound distribution approach.
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Compound and scale mixture of vector and spherical matrix variate elliptical distributions
arXiv: Statistics Theory, 2009Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-jáimezAbstract:Several matrix variate Hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted Hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted Hypergeometric type distributions is also derived as a particular case of the compound distribution approach.
Jinfa Cheng - One of the best experts on this subject based on the ideXlab platform.
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on the complex difference equation of Hypergeometric type on non uniform lattices
Acta Mathematica Sinica, 2020Co-Authors: Jinfa ChengAbstract:In this article, we obtain a new fundamental theorems for Nikiforov–Uvarov–Suslov complex difference equation of Hypergeometric type by the method of Euler integral transformation, its expression is different from Suslov’s Theorem. We also establish the adjoint equation for Nikiforov–Uvarov–Suslov difference equation of Hypergeometric type on non-uniform lattices, and prove it to be a difference equation of Hypergeometric type on non-uniform lattices as well. The particular solutions of the adjoint equation are then obtained. As an appliction of these particular solutions, we use them to obtain the particular solutions for the original difference equation of Hypergeometric type on non-uniform lattices and other important results.
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Adjoint Difference Equation for a Nikiforov-Uvarov-Suslov difference equation of Hypergeometric type on Non-uniform Lattices.
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Jinfa ChengAbstract:In this article, we establish the adjoint equation for Nikiforov-Uvarov-Suslov difference equation of Hypergeometric type on non-uniform lattices, and prove it to be a difference equation of Hypergeometric type on non-uniform lattices as well. The particular solutions of the adjoint equation are then obtained. As an appliction of these particular solutions, we use them to obtain the particular solutions for the original difference equation of Hypergeometric type on non-uniform lattices. Finally, we prove another kind of fundamental theorems for Nikiforov-Uvarov-Suslov difference equation of Hypergeometric type, which are essentially new results, its expression is different from Suslov's Theorem.
José A. Díaz-garcía - One of the best experts on this subject based on the ideXlab platform.
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Distributions of the compound and scale mixture of vector and spherical matrix variate elliptical distributions
Journal of Multivariate Analysis, 2011Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-jáimezAbstract:Several matrix variate Hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted Hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted Hypergeometric type distributions is also derived as a particular case of the compound distribution approach.
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Compound and scale mixture of vector and spherical matrix variate elliptical distributions
arXiv: Statistics Theory, 2009Co-Authors: José A. Díaz-garcía, Ramón Gutiérrez-jáimezAbstract:Several matrix variate Hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted Hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted Hypergeometric type distributions is also derived as a particular case of the compound distribution approach.
V.p. Spiridonov - One of the best experts on this subject based on the ideXlab platform.
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Introduction to the Theory of Elliptic Hypergeometric Integrals
Partition Functions and Automorphic Forms, 2020Co-Authors: V.p. SpiridonovAbstract:We give a brief account of the key properties of elliptic Hypergeometric integrals—a relatively recently discovered top class of transcendental special functions of Hypergeometric type. In particular, we describe an elliptic generalization of Euler’s and Selberg’s beta integrals, elliptic analogue of the Euler–Gauss Hypergeometric function and some multivariable elliptic Hypergeometric functions on root systems. The elliptic Fourier transformation and corresponding integral Bailey lemma technique is outlined together with a connection to the star-triangle relation and Coxeter relations for a permutation group. We review also the interpretation of elliptic Hypergeometric integrals as superconformal indices of four dimensional supersymmetric quantum field theories and corresponding applications to Seiberg type dualities.
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Aspects of elliptic Hypergeometric functions
arXiv: Classical Analysis and ODEs, 2013Co-Authors: V.p. SpiridonovAbstract:General elliptic Hypergeometric functions are defined by elliptic Hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss Hypergeometric function and Selberg integral, as well as elliptic extensions of many other plain Hypergeometric and $q$-Hypergeometric constructions. In particular, the Bailey chain technique, used for proving Rogers-Ramanujan type identities, has been generalized to integrals. At the elliptic level it yields a solution of the Yang-Baxter equation as an integral operator with an elliptic Hypergeometric kernel. We give a brief survey of the developments in this field.
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Elliptic Hypergeometric terms
arXiv: Classical Analysis and ODEs, 2010Co-Authors: V.p. SpiridonovAbstract:General structure of the multivariate plain and q-Hypergeometric terms and univariate elliptic Hypergeometric terms is described. Some explicit examples of the totally elliptic Hypergeometric terms leading to multidimensional integrals on root systems, either computable or obeying non-trivial symmetry transformations, are presented.
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essays on the theory of elliptic Hypergeometric functions
Russian Mathematical Surveys, 2008Co-Authors: V.p. SpiridonovAbstract:This is a brief survey of the main results of the theory of elliptic Hypergeometric functions -- a new class of special functions of mathematical physics. A proof is given of the most general known univariate exact integration formula generalizing Euler's beta integral. It is called the elliptic beta integral. An elliptic analogue of the Gauss Hypergeometric function is constructed together with the elliptic Hypergeometric equation for it. Biorthogonality relations for this function and its particular subcases are described. The known elliptic beta integrals on root systems are listed, and symmetry transformations are considered for the corresponding higher-order elliptic Hypergeometric functions.
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essays on the theory of elliptic Hypergeometric functions
arXiv: Classical Analysis and ODEs, 2008Co-Authors: V.p. SpiridonovAbstract:We give a brief review of the main results of the theory of elliptic Hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's beta integral, which is called the elliptic beta integral. An elliptic analogue of the Gauss Hypergeometric function is constructed together with the elliptic Hypergeometric equation for it. Biorthogonality relations for this function and its particular subcases are described. We list known elliptic beta integrals on root systems and consider symmetry transformations for the corresponding elliptic Hypergeometric functions of the higher order.
Akihito Ebisu - One of the best experts on this subject based on the ideXlab platform.
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Special Values of the Hypergeometric Series
2017Co-Authors: Akihito EbisuAbstract:In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) Hypergeometric series, the generalized Hypergeometric series and the Appell-Lauricella Hypergeometric series. Furthermore, using this method, we get identities for the Hypergeometric series F(a,b;c;x); we show that values of F(a,b;c;x) at some points x can be expressed in terms of gamma functions, together with certain elementary functions. We tabulate the values of F(a,b;c;x) that can be obtained with this method. We find that this set includes almost all previously known values and many previously unknown values.
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Special values of the Hypergeometric series
arXiv: Classical Analysis and ODEs, 2013Co-Authors: Akihito EbisuAbstract:In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) Hypergeometric series, the generalized Hypergeometric series and the Appell-Lauricella Hypergeometric series. Furthermore, using this method, we get identities for the Hypergeometric series $F(a,b;c;x)$; we show that values of $F(a,b;c;x)$ at some points $x$ can be expressed in terms of gamma functions, together with certain elementary functions. We tabulate the values of $F(a,b;c;x)$ that can be obtained with this method. We find that this set includes almost all previously known values and many previously unknown values. Key Words and Phrases: Hypergeometric series, three term relation, special value, solving polynomial systems.
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On a strange evaluation of the Hypergeometric series by Gosper. II
arXiv: Classical Analysis and ODEs, 2012Co-Authors: Akihito EbisuAbstract:There are many identities for the Hypergeometric series presented in the article "Special values of the Hypergeometric series" by Ebisu. In this note, we obtain a new Hypergeometric identity, which includes some of these identities as special cases. We notice that this identity closely relates to a strange evaluation by Gosper. Key Words and Phrases: the Hypergeometric series, Hypergeometric identity.
