Clebsch-Gordan coefficients and special function identities. II. The rotation and Lorentz groups in 3-space

It is shown that the construction of concrete models of Clebsch-Gordan decompositions for tensor products of irreducible group representations leads to a wide variety of special function identities. In this paper the repre-sentation theory of the rotation and Lorentz groups in 3-space is used to give elegant derivations of identities involving Laguerre, Gegenbauer, hypergeometric, and generalized hypergeometric functions. Some of these identities may be new in this general form.