Special Functions and the Theory of Group Representations

Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1968 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.