In 1991-1993 our three-volume book "Representation of Lie Groups and
Spe- cial Functions" was published. When we started to write that book
(in 1983), editors of "Kluwer Academic Publishers" expressed their wish
for the book to be of encyclopaedic type on the subject. Interrelations
between representations of Lie groups and special functions are very
wide. This width can be explained by existence of different types of Lie
groups and by richness of the theory of their rep- resentations. This is
why the book, mentioned above, spread to three big volumes. Influence of
representations of Lie groups and Lie algebras upon the theory of
special functions is lasting. This theory is developing further and
methods of the representation theory are of great importance in this
development. When the book "Representation of Lie Groups and Special
Functions", vol. 1-3, was under preparation, new directions of the
theory of special functions, connected with group representations,
appeared. New important results were discovered in the traditional
directions. This impelled us to write a continuation of our three-volume
book on relationship between representations and special functions. The
result of our further work is the present book. The three-volume book,
published before, was devoted mainly to studying classical special
functions and orthogonal polynomials by means of matrix elements,
Clebsch-Gordan and Racah coefficients of group representations and to
generaliza- tions of classical special functions that were dictated by
matrix elements of repre- sentations.
