By N.Ja. Vilenkin, A.U. Klimyk

This can be the 1st of 3 significant volumes which current a complete remedy of the speculation of the most periods of specified services from the perspective of the speculation of crew representations. This quantity offers with the homes of classical orthogonal polynomials and exact capabilities that are on the topic of representations of teams of matrices of moment order and of teams of triangular matrices of 3rd order. This fabric types the root of many effects touching on classical detailed capabilities reminiscent of Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric features, and various periods of orthogonal polynomials, together with these having a discrete variable. Many new effects are given. the quantity is self-contained, due to the fact an introductory part provides easy required fabric from algebra, topology, useful research and crew thought. For examine mathematicians, physicists and engineers.