Multiple Wilson and Jacobi-Piñeiro polynomials

نویسندگان

  • B. Beckermann
  • J. Coussement
  • W. Van Assche
چکیده

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 T.H. Koornwinder. Here we need to introduce Jacobi and JacobiPiñeiro 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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تاریخ انتشار 2003