2003/03/07 by B. Beckermann, J. Coussement, W. Van Assche · 1 citation
Mathematics · #math.CA #msc:33C45 #msc:42C05
published as J. Approx. Theory 132 (2005), 155-181 · 22 pages, 2 figures
arxiv created 2003/03/07 · arxiv updated 2013/10/04
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.