This 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

Representation of Lie groups and special functions PDF

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