Integral and series representations of special functions related to the group SO(2, 2)

In this sequel to our earlier works [3, 14, 15], we aim to present certain integral and series representations for special functions by using some different group theoretical methods as follows: Restrictions of the representation matrix elements to some block-diagonal matrices; Poisson transform intertwining two realizations of the SO(2, 2)-representation; Invariant properties of the bilinear integral functionals which are used to obtain the matrix elements of bases transforms operators.