Wilson function transforms related to Racah coefficients

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dc.creatorGroenevelt, Wolter
dc.date2005-01-28
dc.date.accessioned2026-07-07T07:36:00Z
dc.date.available2026-07-07T07:36:00Z
dc.descriptionThe irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explicit expressions for the Racah coefficients. The Racah coefficients are Wilson polynomials and Wilson functions. This leads to natural interpretations of the Wilson function transforms. As an application several sum and integral identities are obtained involving Wilson polynomials and Wilson functions. We also compute Racah coefficients for $U_q(\su(1,1))$, which turn out to be Askey-Wilson functions and Askey-Wilson polynomials.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/math/0501511
dc.identifierhttp://arxiv.org/abs/math/0501511
dc.identifierActa Appl. Math. 91 (2006), no. 2, 133--191
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120282
dc.subjectClassical Analysis and ODEs
dc.subjectQuantum Algebra
dc.titleWilson function transforms related to Racah coefficients
dc.typetext

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