On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices
| dc.date.accessioned | 2010-08-25T07:53:49Z | |
| dc.date.available | 2010-08-25T07:53:49Z | |
| dc.date.issued | 2010 | |
| dc.identifier.uri | urn:nbn:de:hebis:34-2010082534270 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/2010082534270 | |
| dc.language.iso | eng | |
| dc.rights | Urheberrechtlich geschützt | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject | Askey-Wilson polynomials | eng |
| dc.subject | Non-uniform lattices | eng |
| dc.subject | Difference equations | eng |
| dc.subject | Divided-difference equations | eng |
| dc.subject | Stieltjes function | eng |
| dc.subject.ddc | 510 | |
| dc.subject.msc | 33D45 | eng |
| dc.subject.msc | 39A13 | eng |
| dc.title | On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices | eng |
| dc.type | Preprint | |
| dcterms.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]. | eng |
| dcterms.accessRights | open access | |
| dcterms.creator | Foupouagnigni, Mama | |
| dcterms.creator | Koepf, Wolfram | |
| dcterms.creator | Kenfack Nangho, Maurice | |
| dcterms.creator | Mboutngam, Salifou | |
| dcterms.isPartOf | Mathematische Schriften Kassel ;; 10, 03 | ger |
| dcterms.source.journal | Mathematische Schriften Kassel | ger |
| dcterms.source.volume | 10, 03 |