Continuous Hahn functions as Clebsch-Gordan coefficients

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dc.creatorGroenevelt, Wolter
dc.creatorKoelink, Erik
dc.creatorRosengren, Hjalmar
dc.date2003-02-20
dc.date.accessioned2026-07-07T07:36:34Z
dc.date.available2026-07-07T07:36:34Z
dc.descriptionAn 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.
dc.identifierhttps://arxiv.org/abs/math/0302251
dc.identifierhttp://arxiv.org/abs/math/0302251
dc.identifierTheory and applications of special functions, 221--284, Dev. Math., 13, Springer, New York, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120473
dc.subjectClassical Analysis and ODEs
dc.subjectRepresentation Theory
dc.titleContinuous Hahn functions as Clebsch-Gordan coefficients
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