dorsal/arxiv
View SchemaBilinear generating functions for orthogonal polynomials
| Authors | H. T. Koelink, J. Van der Jeugt |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9704016 |
| URL | https://arxiv.org/abs/q-alg/9704016 |
Abstract
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.
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"abstract": "Using realisations of the positive discrete series representations of the Lie\nalgebra su(1,1) in terms of Meixner-Pollaczek polynomials, the action of\nsu(1,1) on Poisson kernels of these polynomials is considered. In the tensor\nproduct of two such representations, two sets of eigenfunctions of a certain\noperator can be considered and they are shown to be related through continuous\nHahn polynomials. As a result, a bilinear generating function for continuous\nHahn polynomials is obtained involving the Poisson kernel of Meixner-Pollaczek\npolynomials. For the positive discrete series representations of the quantised\nuniversal enveloping algebra Uq(su(1,1)) a similar analysis is performed and\nleads to a bilinear generating function for Askey-Wilson polynomials involving\nthe Poisson kernel of Al-Salam and Chihara polynomials.",
"arxiv_id": "q-alg/9704016",
"authors": [
"H. T. Koelink",
"J. Van der Jeugt"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Bilinear generating functions for orthogonal polynomials",
"url": "https://arxiv.org/abs/q-alg/9704016"
},
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