Hypergeometric Functions Of Several Matrix Arguments

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Hypergeometric Functions Of Several Matrix Arguments

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Author : A. M. Mathai
language : en
Publisher:
Release Date : 1993

Hypergeometric Functions Of Several Matrix Arguments written by A. M. Mathai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Hypergeometric functions categories.

Jacobians Of Matrix Transformation And Functions Of Matrix Arguments

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Author : Arak M Mathai
language : en
Publisher: World Scientific Publishing Company
Release Date : 1997-10-31

Jacobians Of Matrix Transformation And Functions Of Matrix Arguments written by Arak M Mathai and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-31 with Mathematics categories.

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.

Hypergeometric Functions On Domains Of Positivity Jack Polynomials And Applications

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Author : Donald St. P. Richards
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Hypergeometric Functions On Domains Of Positivity Jack Polynomials And Applications written by Donald St. P. Richards and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book is the first set of proceedings to be devoted entirely to the theory of hypergeometric functions defined on domains of positivity. Most of the scientific areas in which these functions are applied include analytic number theory, combinatorics, harmonic analysis, random walks, representation theory, and mathematical physics - are represented here. This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida in March 1991, which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses for it contains many open problems.

Gauss Hypergeometric Function

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Author : Ravi Dwivedi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-02

Gauss Hypergeometric Function written by Ravi Dwivedi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Science categories.

This book presents a novel journey of the Gauss hypergeometric function and contains the different versions of the Gaussian hypergeometric function, including its classical version. In particular, the $q$-Gauss or basic Gauss hypergeometric function, Gauss hypergeometric function with matrix arguments, Gauss hypergeometric function with matrix parameters, the matrix-valued Gauss hypergeometric function, the finite field version, the extended Gauss hypergeometric function, the $(p, q)$- Gauss hypergeometric function, the incomplete Gauss hypergeometric function and the discrete analogue of Gauss hypergeometric function. All these forms of the Gauss hypergeometric function and their properties are presented in such a way that the reader can understand the working algorithm and apply the same for other special functions. This book is useful for UG and PG students, researchers and faculty members working in the field of special functions and related areas.

Representation Of Lie Groups And Special Functions

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Author : Naum I︠A︡kovlevich Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-30

Representation Of Lie Groups And Special Functions written by Naum I︠A︡kovlevich Vilenkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-30 with Mathematics categories.

This is the first of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations.This volume deals with the properties of classical orthogonal polynomials and special functions which are related to representations of groups of matrices of second order and of groups of triangular matrices of third order. This material forms the basis of many results concerning classical special functions such as Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric functions, and different classes of orthogonal polynomials, including those having a discrete variable. Many new results are given.The volume is self-contained, since an introductory section presents basic required material from algebra, topology, functional analysis and group theory.For research mathematicians, physicists and engineers.

Multivariate Normal Distribution The Theory And Applications

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Author : Thu Pham-gia
language : en
Publisher: World Scientific
Release Date : 2021-05-05

Multivariate Normal Distribution The Theory And Applications written by Thu Pham-gia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-05 with Business & Economics categories.

This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.

Multidisciplinary Approach In Research Area Volume 1

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Author : Chief Editor- Biplab Auddya, Editor- Prof Deepali Virmani, Shivam Kumar Upadhyay, Lalit Mohan, Pooja Singh, Dr Pallavi Arya, Dr R. Vijayalakshmi
language : en
Publisher: The Hill Publication
Release Date : 2023-12-12

Multidisciplinary Approach In Research Area Volume 1 written by Chief Editor- Biplab Auddya, Editor- Prof Deepali Virmani, Shivam Kumar Upadhyay, Lalit Mohan, Pooja Singh, Dr Pallavi Arya, Dr R. Vijayalakshmi and has been published by The Hill Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-12 with Antiques & Collectibles categories.

Contributions To Complex Matrix Variate Distributions Theory

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Author : Daya Krishna Nagar
language : en
Publisher: Universidad de Antioquia
Release Date : 2009

Contributions To Complex Matrix Variate Distributions Theory written by Daya Krishna Nagar and has been published by Universidad de Antioquia this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Distribution (Probability theory) categories.

"Random matrices (real or complex) play an important role in the study of multivariate statistical methods. They have been found useful in physics, engineering, economics, psychology and other fields of investigation. Contributions to Complex Matrix Variate Distribution Theory gives a comprehensive coverage of complex random matrices, and defines a number of new complex matrix variate distributions. It also gathers and systematiclly [sic] presents several results on zonal polynomials, invariant polynomials and hypergeometric functions of Hermitian matrices which until now could only be found scattered in various mathematical or statistical journals. This book provides a compact self-contained introduction to the complex matrix variate distribution theory and includes new results that will be a useful source to all those working in the area, stimulate further research, and help advance this field. This book, valuable to researchers, graduate students, and instructors in multivariate statistical analysis, will also interest researchers in a variety of areas including physicists, engineers, psychometricians, and econometricians."--Back cover

Applied Multivariate Analysis

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Author : S. James Press
language : en
Publisher: Courier Corporation
Release Date : 2012-09-05

Applied Multivariate Analysis written by S. James Press and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-05 with Mathematics categories.

Geared toward upper-level undergraduates and graduate students, this two-part treatment deals with the foundations of multivariate analysis as well as related models and applications. Starting with a look at practical elements of matrix theory, the text proceeds to discussions of continuous multivariate distributions, the normal distribution, and Bayesian inference; multivariate large sample distributions and approximations; the Wishart and other continuous multivariate distributions; and basic multivariate statistics in the normal distribution. The second half of the text moves from defining the basics to explaining models. Topics include regression and the analysis of variance; principal components; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations, with particular focus on multidimensional scaling and clustering. In addition to its value to professional statisticians, this volume may also prove helpful to teachers and researchers in those areas of behavioral and social sciences where multivariate statistics is heavily applied. This new edition features an appendix of answers to the exercises.

Representation Theory And Noncommutative Harmonic Analysis Ii

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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Representation Theory And Noncommutative Harmonic Analysis Ii written by A.A. Kirillov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the prob ability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions. They are doubly periodic functions of a complex variable. This periodicity has led to consideration of the lattice of periods and to linear-fractional trans formations of the complex plane which leave this lattice invariant. The group of these transformations is isomorphic to the quotient group of the group 8L(2, Z) of unimodular matrices of the second order with integral elements with respect to its center. Investigation of properties of elliptic functions led to the study of automorphic functions and forms. This gave the first connec tion between the theory of groups and this important class of functions. The further development of the theory of automorphic functions was related to geometric concepts connected with the fact that the group of linear-fractional transformations with real elements can be realized as the group of motions of th the Lobachevskij plane. We also note that at the beginning of the 19 century Gauss used the group 8L(2, Z) in his papers on the theory of indeterminate quadratic forms.