Multiple Wilson and Jacobi–Piñeiro polynomials |
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Authors: | B Beckermann J Coussement W Van Assche |
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Institution: | aLaboratoire de Mathématiques P. Painlevé UMR 8524 (ANO), UFR Mathématiques - M3, Université de Lille 1, 59655 Villeneuve d’Ascq CEDEX, France;bDepartment of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium |
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Abstract: | We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite–Padé polynomials) of type II. These polynomials can be written as a Jacobi–Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by Koornwinder. Here we need to introduce Jacobi and Jacobi–Piñeiro polynomials with complex parameters. Some explicit formulas are provided for both Jacobi–Piñeiro and multiple Wilson polynomials, one of them in terms of Kampé de Fériet series. Finally, we look at some limiting relations and construct a part of a multiple AT-Askey table. |
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Keywords: | Multiple orthogonal polynomials Hypergeometric functions |
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