Multiple Wilson and Jacobi-Piñeiro polynomials

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.