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.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.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, eng the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in  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 , see also . 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 ger dcterms.isPartOf 10, 03 ger dc.subject.msc 33D45 eng dc.subject.msc 39A13 eng
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