Abstract
An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial 3 F 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.
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Groenevelt, W., Koelink, E., Rosengren, H. (2005). Continuous Hahn Functions as Clebsch-Gordan Coefficients. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_11
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