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Special Functions and the Theory of Group Representations
 
Special Functions and the Theory of Group Representations
Softcover ISBN:  978-0-8218-1572-4
Product Code:  MMONO/22
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4439-6
Product Code:  MMONO/22.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-1572-4
eBook: ISBN:  978-1-4704-4439-6
Product Code:  MMONO/22.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Special Functions and the Theory of Group Representations
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Special Functions and the Theory of Group Representations
Softcover ISBN:  978-0-8218-1572-4
Product Code:  MMONO/22
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4439-6
Product Code:  MMONO/22.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-1572-4
eBook ISBN:  978-1-4704-4439-6
Product Code:  MMONO/22.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 221968; 613 pp
    MSC: Primary 33; Secondary 22;

    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Group representations
    • The additive group of real numbers and the exponential function. Fourier series and integrals
    • The group of second order unitary matrices and the polynomials of Legendre and Jacobi
    • Representations of the group of motions of the plane and Bessel functions
    • Representations of the group of motions of the pseudo-euclidean plane and the functions of Bessel and Macdonald
    • Representations of the group $QU(2)$ of unimodular quasi-unitary matrices of the second order and the functions of Legendre and Jacobi
    • Representations of the group of real unimodular matrices and the hypergeometric function
    • Representations of the group of third order triangular matrices and the Whittaker functions
    • The group of rotations of $n$-dimensional euclidean space and Gegenbauer functions
    • Representations of the group of hyperbolic rotations of $n$-dimensional space and Legendre functions
    • The group of motions of the $n$-dimensional euclidean space and Bessel functions
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 221968; 613 pp
MSC: Primary 33; Secondary 22;

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.

  • Chapters
  • Introduction
  • Group representations
  • The additive group of real numbers and the exponential function. Fourier series and integrals
  • The group of second order unitary matrices and the polynomials of Legendre and Jacobi
  • Representations of the group of motions of the plane and Bessel functions
  • Representations of the group of motions of the pseudo-euclidean plane and the functions of Bessel and Macdonald
  • Representations of the group $QU(2)$ of unimodular quasi-unitary matrices of the second order and the functions of Legendre and Jacobi
  • Representations of the group of real unimodular matrices and the hypergeometric function
  • Representations of the group of third order triangular matrices and the Whittaker functions
  • The group of rotations of $n$-dimensional euclidean space and Gegenbauer functions
  • Representations of the group of hyperbolic rotations of $n$-dimensional space and Legendre functions
  • The group of motions of the $n$-dimensional euclidean space and Bessel functions
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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