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Title: On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices
Authors: Foupouagnigni, MamaKoepf, WolframKenfack Nangho, MauriceMboutngam, Salifou
???metadata.dc.subject.ddc???: 510 - Mathematik (Mathematics)
Issue Date: 2010
Series/Report no.: Mathematische Schriften Kassel10, 03
Abstract: The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].
URI: urn:nbn:de:hebis:34-2010082534270
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