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Special Functions and the Theory of Group Representations
About this Title
N. Ja. Vilenkin. Translated by V. N. Singh
Publication: Translations of Mathematical Monographs
Publication Year:
1968; Volume 22
ISBNs: 978-0-8218-1572-4 (print); 978-1-4704-4439-6 (online)
DOI: https://doi.org/10.1090/mmono/022
MathSciNet review: MR0229863
MSC: Primary 33.00; Secondary 22.00
Table of Contents
Front/Back Matter
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