On the representations of the groups SO(3), O(2, 1), and M(2) defined in terms of Lamé, Mathieu,and parabolic functions

Products of Mathieu, parabolic-cylinder and Lamé functions appear as basis functions for the irreducible representations of the groups M(2), O(2,1) and SO(3). Addition formulas concerning the Mathieu functions, parabolic cylinder functions, and Lamé polynomials are recovered or obtained.