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Representation of Lie Groups and Special Functions

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

  • Book
  • © 1991

Overview

Authors:
  1. N. Ja. Vilenkin

    1. Institute for Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kiev, USSR

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  2. A. U. Klimyk

    1. Department of Mathematics, The Correspondence Pedagogical Institute, Moscow, USSR

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and its Applications (MASS, volume 72)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Introduction

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 1-5

  3. Elements of the Theory of Lie Groups and Lie Algebras

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 6-67

  4. Group Representations and Harmonic Analysis on Groups

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 68-108

  5. Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 109-164

  6. Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 165-206

  7. Representations of Groups of Third Order Triangular Matrices, the Confluent Hypergeometric Function, and Related Polynomials and Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 207-268

  8. Representations of the Groups SU(2), SU(1,1) and Related Special Functions: Legendre, Jacobi, Chebyshev Polynomials and Functions, Gegenbauer, Krawtchouk, Meixner Polynomials

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 269-373

  9. Representations of the Groups SU(1,1) and SL(2, ℝ) in Mixed Bases. The Hypergeometric Function

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 374-497

  10. Clebsch-Gordan Coefficients, Racah Coefficients, and Special Functions

    • N. Ja. Vilenkin, A. U. Klimyk
    Pages 498-594

  11. Back Matter

    Pages 595-608
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Keywords

Authors and Affiliations

  • Institute for Theoretical Physics, Academy of Sciences of the Ukrainian SSR, Kiev, USSR

    N. Ja. Vilenkin

  • Department of Mathematics, The Correspondence Pedagogical Institute, Moscow, USSR

    A. U. Klimyk

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