Bilinear generating functions for orthogonal polynomials

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dc.creatorKoelink, H. T.
dc.creatorVan der Jeugt, J.
dc.date1997-04-24
dc.date.accessioned2026-07-07T09:17:33Z
dc.date.available2026-07-07T09:17:33Z
dc.descriptionUsing 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.
dc.description18 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/q-alg/9704016
dc.identifierhttp://arxiv.org/abs/q-alg/9704016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153704
dc.subjectQuantum Algebra
dc.titleBilinear generating functions for orthogonal polynomials
dc.typetext

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