Abstract:
There are many ways to define multiple orthogonal polynomials with respect to the classical
continuous weights. The approach as in [1,2,3] preserves a kind of the
Rodrigues formula, which is a very useful property. We focus on adapting this approach for the
discrete case — bearing in mind the deep connection between the classical discrete and
continuous orthogonality.
The talk is devoted to a new class of polynomials of multiple orthogonality with respect to the
product of classical discrete weights on integer lattices with noninteger shifts. We obtain
explicit representations in the form of the Rodrigues formulas. The case of two weights will be
presented in more detail.
This is a joint work with A. Dyachenko (UCL Department of Mathematics, Gower St, London, United Kingdom).
Language: English
References
A. I. Aptekarev, “Multiple orthogonal polynomials”, Proceedings of the VIII Symposium on Orthogonal Polynomials and Their Applications (Seville, 1997), 99, no. 1-2, 1998, 423–447
A. I. Aptekarev, F. Marcellán, I. A. Rocha, “Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials”, J. Approx. Theory, 90:1 (1997), 117–146
Walter Van Assche, Els Coussement, “Some classical multiple orthogonal polynomials”, J. Comput. Appl. Math., 127:1-2 (2001), 317–347
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