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Special Functions and the Theory of Group Representations
N. Ja. Vilenkin
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Translations of Mathematical Monographs
1968; 613 pp; softcover
Volume: 22
Reprint/Revision History:
reprinted with corrections 1983; fifth printing 2000
ISBN-10: 0-8218-1572-5
ISBN-13: 978-0-8218-1572-4
List Price: US$135
Member Price: US$108
Order Code: MMONO/22
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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.

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