## Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie Groups, Special Functions and Integral TransformsThis 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

6 | |

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 |

595 | |

### Other editions - View all

Representation of Lie Groups and Special Functions N. Ja. Vilenkin,A. U. Klimyk No preview available - 1991 |

Representation of Lie Groups and Special Functions: Volume 1: Simplest Lie ... N.Ja. Vilenkin,A.U. Klimyk No preview available - 2012 |

### Common terms and phrases

a-Hico algebra g analog analytic continuation automorphism called CGC’s Charlier polynomials coefficients commutative compact group connected converges cosh decomposition defined derive differential equation direct sum equality equivalent Example expansion expression finite dimensional representations follows from formula Fourier transform function f g e G Hence Hermitian Hilbert space homogeneous space hypergeometric function implies infinitesimal operators integral representation invariant with respect inversion formula irreducible representations isomorphic kernels Laplace Lie algebra Lie group Lie group G linear space linear transformations mapping matrix matrix elements Mellin transform obtain one-parameter subgroups orthogonal orthonormal basis parameters prove recurrence relations regular representation replace representation of G representations TR right hand side right shifts scalar product Section semisimple sinh sinhº ſº SO(n space of functions subalgebra subspace substitution symmetry relations tanh tensor product unitary representations values vector