Special functions and the complex Euclidean group in 3-space. III

This paper is the third in a series analyzing identities for special functions which can be derived from a study of the local representations of the Euclidean group in 3-space. Here identities are derived which relate Gegenbauer polynomials, Whittaker functions, Jacobi polynomials, and Bessel functions. Among the results are generalizations of the addition theorems for solid-spherical harmonics and a group-theoretic interpretation of the Maxwell theory of poles.