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Generalized Hypergeometric Functions With Applications In Statistics And Physical Sciences
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Book Synopsis Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences by : A. M. Mathai
Download or read book Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences written by A. M. Mathai and published by Springer. This book was released on 2006-11-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences by : A. M. Mathai
Download or read book Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences written by A. M. Mathai and published by . This book was released on 2014-01-15 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Hypergeometric Functions by : Lucy Joan Slater
Download or read book Generalized Hypergeometric Functions written by Lucy Joan Slater and published by Cambridge University Press. This book was released on 1966-01-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions. The unified theory provides a means for the analysis of the simpler functions and can be used to solve the more complicated equations in physics. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory. Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel series. This book was planned jointly with the late Professor W. N. Bailey as an extended revision of his Cambridge Mathematical Tract (1935) on the subject and Dr Slater has continued it single-handed since Professor Bailey's death, incorporating in it the results of many of her own researches.
Book Synopsis Special Functions for Applied Scientists by : A.M. Mathai
Download or read book Special Functions for Applied Scientists written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2008-02-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.
Book Synopsis A Handbook of Generalized Special Functions for Statistical and Physical Sciences by : A. M. Mathai
Download or read book A Handbook of Generalized Special Functions for Statistical and Physical Sciences written by A. M. Mathai and published by Oxford University Press, USA. This book was released on 1993 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complicated generalized special functions such as Meijer's G-functions and functions of matrix arguments are here presented at a level suitable for every potential user. This handbook is thus a valuable reference source and a manual for researchers and advanced students in mathematical statistics, mathematical physics, several branches of mathematics, engineering problems, econometrics, and various applied areas where transcendental functions are used.
Book Synopsis Generalized Hypergeometric Equation by : K Srinivasa Rao
Download or read book Generalized Hypergeometric Equation written by K Srinivasa Rao and published by Iph001. This book was released on 2018-10-24 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aims and objectives of this book are to present a unified approach to the study of special functions of mathematics, which are ubiquitous and essential to a formulation of any physical or engineering problem in a mathematical format. In this detailed monograph, the second order Ordinary Differential Equation of Carl Friedrich Gauss is the starting point for the study of special functions. This is a simple, unified and novel approach to the treatment of the subject. The new feature in this presentation is that of the group theory associated with special functions. Generalized Hypergeometric Functions: Transformations and group theoretical aspects outlines the important relationship between the Gauss hypergeometric equation and corresponding special functions. Each chapter details the application of group theory to the study of special functions and discusses various transformations, group theory, and their relevance In various applications. It is a relatively self-contained book that includes extensive introductory expositions of group theory. Offering an original approach to the hypergeometric equation and related function, this book is important for fundamental understanding of the mathematics underlying various aspects of physics, applied mathematics, and engineering. With the use of worked examples, proofs, summaries and references, this work can be used in various courses of study and research, and it is also useful for self-study. Book jacket.
Download or read book The H-Function written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2009-10-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Book Synopsis Hypergeometric Functions and Their Applications by : James B. Seaborn
Download or read book Hypergeometric Functions and Their Applications written by James B. Seaborn and published by . This book was released on 1991-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the special functions of applied mathematics can be expressed in terms of hypergeometric functions. In this book each special function is seen to arise in one or more physical contexts as a solution of a differential equation that can be transformed into a hypergeometric equation. The special function is then defined in terms of a generalized hypergeometric function and the equivalence to alternate definitions is established. Many of the interesting and important properties of the special functions that one encounters in standard upper level textbooks on engineering, they physical sciences, and other branches of applied mathematics are derived. The close connection of the development with applications is emphasized throughout the book in the text and in the exercises.
Book Synopsis Mittag-Leffler Functions, Related Topics and Applications by : Rudolf Gorenflo
Download or read book Mittag-Leffler Functions, Related Topics and Applications written by Rudolf Gorenflo and published by Springer Nature. This book was released on 2020-10-27 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.
Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias
Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.
Book Synopsis Mathematical Analysis and Applications II by : Hari M. Srivastava
Download or read book Mathematical Analysis and Applications II written by Hari M. Srivastava and published by MDPI. This book was released on 2020-03-19 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications” . Investigations involving the theory and applications of mathematical analytical tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.
Book Synopsis Finite Form Representations for Meijer G and Fox H Functions by : Carlos A. Coelho
Download or read book Finite Form Representations for Meijer G and Fox H Functions written by Carlos A. Coelho and published by Springer Nature. This book was released on 2019-12-13 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book depicts a wide range of situations in which there exist finite form representations for the Meijer G and the Fox H functions. Accordingly, it will be of interest to researchers and graduate students who, when implementing likelihood ratio tests in multivariate analysis, would like to know if there exists an explicit manageable finite form for the distribution of the test statistics. In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently. The test statistics in question range from common ones, such as those used to test e.g. the equality of means or the independence of blocks of variables in real or complex normally distributed random vectors; to far more elaborate tests on the structure of covariance matrices and equality of mean vectors. The book also provides computational modules in Mathematica®, MAXIMA and R, which allow readers to easily implement, plot and compute the distributions of any of these statistics, or any other statistics that fit into the general paradigm described here.
Book Synopsis Multivariate Normal Distribution, The: Theory And Applications by : Thu Pham-gia
Download or read book Multivariate Normal Distribution, The: Theory And Applications written by Thu Pham-gia and published by World Scientific. This book was released on 2021-05-05 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Special Functions by : Richard Beals
Download or read book Special Functions written by Richard Beals and published by Cambridge University Press. This book was released on 2010-08-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
Book Synopsis Bilinear Forms and Zonal Polynomials by : Arak M. Mathai
Download or read book Bilinear Forms and Zonal Polynomials written by Arak M. Mathai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms. The book is mostly self-contained. It starts from basic principles and brings the readers to the current research level in these areas. It is developed with detailed proofs and illustrative examples for easy readability and self-study. Several exercises are proposed at the end of the chapters. The complicated topic of zonal polynomials is explained in detail in this book. The book concentrates on the theoretical developments in all the topics covered. Some applications are pointed out but no detailed application to any particular field is attempted. This book can be used as a textbook for a one-semester graduate course on quadratic and bilinear forms and/or on zonal polynomials. It is hoped that this book will be a valuable reference source for graduate students and research workers in the areas of mathematical statistics, quadratic and bilinear forms and their generalizations, zonal polynomials, invariant polynomials and related topics, and will benefit statisticians, mathematicians and other theoretical and applied scientists who use any of the above topics in their areas. Chapter 1 gives the preliminaries needed in later chapters, including some Jacobians of matrix transformations. Chapter 2 is devoted to bilinear forms in Gaussian real ran dom vectors, their properties, and techniques specially developed to deal with bilinear forms where the standard methods for handling quadratic forms become complicated.
Book Synopsis The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by : Thanh Hai Nguyen
Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Thanh Hai Nguyen and published by World Scientific. This book was released on 1992 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
Book Synopsis The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by : Nguyen Thanh Hai
Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Nguyen Thanh Hai and published by World Scientific. This book was released on 1992-05-26 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables. A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals. Contents:General H-Function of Two Variables and the Solution of its Convergence ProblemMain Properties, Series Presentations and Characteristic of the H-FunctionH-Function with the Third Characteristic and its Particular CasesG-Function of Two VariablesTable of Special Cases of the G-FunctionOne-Dimensional H-Transform in Spaces M-1(L) and M-1c,γ(L) and its Composition StructureClassical Laplace Convolution and its New PropertiesGeneral Integral Convolution for H-Function TransformExistence and Factorization Property of the ConvolutionNew Examples of Convolution for Classical Integral TransformsGeneralized Integral ConvolutionGeneral Leibniz Rules and Their Integral Analogs Readership: Researchers and students in mathematics, mechanics and physics. keywords:Mellin Transform of the One and Two Variables;Mellin-Barnes Integrals;Convolutions;Meijer's G-Function of Two Variables;Fox's H-Function of Two Variables;Fourier Transform;Laplace Transform;Gamma Function;Double Kampe de Feriet Hypergeometric Series;Leibniz Rules and Integral Analogs“The book gives a detailed and rigorous account of the theory of double Mellin-Barnes type integrals and contains new fundamental results and their applications to convolution theory. It is a valuable addition to the existing literature in the field of special functions and integral transforms.”K M Saksena “In the areas of special functions and integral transforms, teachers, researchers and graduate students are advised to refer to this work.” Siam Review
