Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 612 pages
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.
 

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Contents

Elements of the Theory of Lie Groups and
6
List of the Most Important Notations
9
Quantum Groups qOrthogonal Polynomials and Basic Hypergeometric Functions
14
Following the publication of the book Special Functions and the Theory
30
Group Representations and Harmonic Analysis
68
6
70
Chapter
109
7
145
Chapter
207
Chapter
269
Chapter
374
Transforms
475
Chapter
494
Jacobi Polynomials
517
Wilson polynomials
559
Bibliography
595

Chapter
165
8
182

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