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

ISBN-13: 9789401055666 / Angielski / Miękka / 2012 / 612 str.

N. Ja Vilenkin; A. U. Klimyk

Opis

One service mathematici has rendered the 'Et moi, ...* si j'avait IU comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belong., on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', Eric T. Bell able to do something with it. O. H eaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other pans and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'el;re of this series.

Spis treści

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.