Multiple Wilson and Jacobi--Piòeiro polynomials

Authors:
B. Beckermann;J. Coussement;W. Van Assche
Affiliations:
Laboratoire de Mathématiques P. Painlevé UMR 8524 (ANO), UFR Mathématiques - M3, Université de Lille 1, 59655 Villeneuve d'Ascq CEDEX, France;Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium;Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Venue:
Journal of Approximation Theory
Year:
2005

Citing 7
Cited 1

Asymptotics for the 4F3 polynomials

Journal of Approximation Theory
Multiple orthogonal polynomials

Journal of Computational and Applied Mathematics
Some classical multiple orthogonal polynomials

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Some properties of multiple orthogonal polynomials associated with Macdonald functions

Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
Some discrete multiple orthogonal polynomials

Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Gaussian quadrature for multiple orthogonal polynomials

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Full length article: Multiple Meixner-Pollaczek polynomials and the six-vertex model

Journal of Approximation Theory

Quantified Score

Hi-index	0.01

Visualization

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 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.