1997/04/24 by H.T. Koelink, H. T. Koelink, Koelink, H. T. +2 · 1 citation
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9704016
18 pages, LaTeX
arxiv created 1997/04/24 · openalex publication_date 1997/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using realisations of the positive discrete series representations of the Lie algebra su(1,1) in terms of Meixner-Pollaczek polynomials, the action of su(1,1) on Poisson kernels of these polynomials is considered. In the tensor product of two such representations, two sets of eigenfunctions of a certain operator can be considered and they are shown to be related through continuous Hahn polynomials. As a result, a bilinear generating function for continuous Hahn polynomials is obtained involving the Poisson kernel of Meixner-Pollaczek polynomials. For the positive discrete series representations of the quantised universal enveloping algebra Uq(su(1,1)) a similar analysis is performed and leads to a bilinear generating function for Askey-Wilson polynomials involving the Poisson kernel of Al-Salam and Chihara polynomials.