  The decomposition of the tensor product of a positive and a negative discrete
series representation of the Lie algebra su(1,1) is a direct integral over the
principal unitary series representations. In the decomposition discrete terms
can occur, and the discrete terms are a finite number of discrete series
representations or one complementary series representation. The interpretation
of Meixner functions and polynomials as overlap coefficients in the four
classes of representations and the Clebsch-Gordan decomposition, lead to a
general bilinear generating function for the Meixner polynomials. Finally,
realizing the positive and negative discrete series representations as
operators on the spaces of holomorphic and anti-holomorphic functions
respectively, a non-symmetric type Poisson kernel is found for the Meixner
functions.
