  An explicit bilinear generating function for Meixner-Pollaczek polynomials is
proved. This formula involves continuous dual Hahn polynomials,
Meixner-Pollaczek functions, and non-polynomial $_3F_2$-hypergeometric
functions that we consider as continuous Hahn functions. An integral transform
pair with continuous Hahn functions as kernels is also proved. These results
have an interpretation for the tensor product decomposition of a positive and a
negative discrete series representation of $\su(1,1)$ with respect to
hyperbolic bases, where the Clebsch-Gordan coefficients are continuous Hahn
functions.
