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Multiple Wilson and Jacobi-Pineiro polynomials

B. Beckermann·J. Coussement·W. Van Assche
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Abstract

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Pade polynomials) of type II. These polynomials can be written as a Jacobi-Pineiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and Jacobi-Pineiro polynomials with complex parameters. Some explicit formulas are provided for both Jacobi-Pineiro and multiple Wilson polynomials, one of them in terms of Kampe de Feriet series. Finally we look at some limiting relations and construct a part of a multiple AT-Askey table.

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B. Beckermann, J. Coussement, W. Van Assche. 2003-03-07. Multiple Wilson and Jacobi-Pineiro polynomials. https://arxiv.org/abs/math/0303093

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