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Representation of lie groups, special functions and integral transforms VOL 1 : simplest lie groups (Maths and its applications, Soviet series 72), Softcover reprint of the original 1st ed. 1991 Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms Mathematics and its Applications Series, Vol. 72

Langue : Anglais

Auteurs :

Couverture de l’ouvrage Representation of lie groups, special functions and integral transforms VOL 1 : simplest lie groups (Maths and its applications, Soviet series 72)
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.
Series Editor's Preface. Preface. List of Special Symbols. 0: Introduction. 1: Elements of the Theory of Lie Groups and Lie Algebras. 2: Group Representations and Harmonic Analysis on Groups. 3: Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions. 4: Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions. 5: Representations of Groups of Third Order Triangular Matrices, the Confluent Hypergeometric Function and Related Polynomials and Functions. 6: Representations of the Groups SU (2), SU (1,1) and Related Special Functions: Legendre, Jacobi, Chebyshev Polynomials and Functions, Gegenbauer, Krawtchouk, Meixner Polynomials. 7: Representations of the Groups SU (1,1) and SL (2, R) in Mixed Bases. The Hypergeometric Function. 8: Clebsch-Gordan Coefficients, Racah Coefficients, and Special Functions. Bibliography. Subject Index.

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