Journal of approximation theory vol:132 issue:2 pages:155-181
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 Koorn-winder. 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. (C) 2005 Elsevier Inc. All rights reserved.