Lie Theory And Special Functions
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Lie Theory And Special Functions
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Author : Miller
language : en
Publisher: Academic Press
Release Date : 1968
Lie Theory And Special Functions written by Miller and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Lie Theory and Special Functions
Representation Of Lie Groups And Special Functions
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Author : N.Ja. Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Representation Of Lie Groups And Special Functions written by N.Ja. 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 2013-04-17 with Mathematics categories.
In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.
Representation Of Lie Groups And Special Functions
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Author : N.Ja. Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Representation Of Lie Groups And Special Functions written by N.Ja. 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 2012-12-06 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.
Special Functions And The Theory Of Group Representations
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Author : Naum I͡Akovlevich Vilenkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Special Functions And The Theory Of Group Representations written by Naum I͡Akovlevich Vilenkin 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 1978 with Mathematics categories.
Lie Theory And Special Functions Special Functions
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Author : Willard Miller
language : en
Publisher:
Release Date : 1968
Lie Theory And Special Functions Special Functions written by Willard Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Special Functions And The Theory Of Group Representations
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Author : Naum I͡Akovlevich Vilenkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Special Functions And The Theory Of Group Representations written by Naum I͡Akovlevich Vilenkin 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 1968 with Mathematics categories.
A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.
Special Functions For Applied Scientists
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Author : A.M. Mathai
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-13
Special Functions For Applied Scientists written by A.M. Mathai 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 2008-02-13 with Science categories.
Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introduction to statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed. Their applications to reaction-diffusion problems in physics, input-output analysis, and Mittag-Leffler stochastic processes are developed. Chapter 3 deals with q-hyper-geometric or basic hypergeometric functions. Chapter 4 covers basic hypergeometric functions and Ramanujan's work on elliptic and theta functions. Chapter 5 examines the topic of special functions and Lie groups. Chapters 6 to 9 are devoted to applications of special functions. Applications to stochastic processes, geometric infinite divisibility of random variables, Mittag-Leffler processes, alpha-Laplace processes, density estimation, order statistics and astrophysics problems, are dealt with in Chapters 6 to 9. Chapter 10 is devoted to wavelet analysis. An introduction to wavelet analysis is given. Chapter 11 deals with the Jacobians of matrix transformations. Various types of matrix transformations and the associated Jacobians are provided. Chapter 12 is devoted to the discussion of functions of matrix argument in the real case. Functions of matrix argument and the pathway models along with their applications are discussed.
Theory And Application Of Special Functions
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Author : Richard Askey
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Theory And Application Of Special Functions written by Richard Askey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.
Lie Theory And Special Functions
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Author : Willard Miller
language : en
Publisher:
Release Date : 1968
Lie Theory And Special Functions written by Willard Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Functions, Special categories.
Representation Of Lie Groups And Special Functions
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Author : N. Ja. Vilenkin
language : en
Publisher:
Release Date : 2014-01-15
Representation Of Lie Groups And Special Functions written by N. Ja. Vilenkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.