The Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. III

Along the lines of two previous papers, the Clebsch‐Gordan problem for products of representations of SU(1, 1) of the form $D^{+}\mathrm{\otimes \; C}$ is related to the properties of the Lorentz group O(3, 1). The structure of the Clebsch‐Gordan series for this case is understood in a new way as being due to the properties of O(3, 1) spherical harmonics on the timelike and spacelike hyperboloids in Minkowski space. The Clebsch‐Gordan coefficients in a continuous basis are then evaluated.